# Statistics

• ADTEST Anderson-Darling Test of Normality
• AVEDEV average of the absolute deviations of a data set
• AVERAGE average of all the numeric values and cells
• AVERAGEA average of all the values and cells
• BERNOULLI probability mass function of a Bernoulli distribution
• BETA.DIST cumulative distribution function of the beta distribution
• BETADIST cumulative distribution function of the beta distribution
• BETAINV inverse of the cumulative distribution function of the beta distribution
• BINOM.DIST.RANGE probability of the binomial distribution over an interval
• BINOMDIST probability mass or cumulative distribution function of the binomial distribution
• CAUCHY probability density or cumulative distribution function of the Cauchy, Lorentz or Breit-Wigner distribution
• CHIDIST survival function of the chi-squared distribution
• CHIINV inverse of the survival function of the chi-squared distribution
• CHITEST p value of the Goodness of Fit Test
• CONFIDENCE margin of error of a confidence interval for the population mean
• CONFIDENCE.T margin of error of a confidence interval for the population mean using the Student's t-distribution
• CORREL Pearson correlation coefficient of two data sets
• COUNT total number of integer or floating point arguments passed
• COUNTA number of arguments passed not including empty cells
• COVAR covariance of two data sets
• COVARIANCE.S sample covariance of two data sets
• CRITBINOM right-tailed critical value of the binomial distribution
• CRONBACH Cronbach's alpha
• CVMTEST Cramér-von Mises Test of Normality
• DEVSQ sum of squares of deviations of a data set
• EXPONDIST probability density or cumulative distribution function of the exponential distribution
• EXPPOWDIST the probability density function of the Exponential Power distribution
• FDIST survival function of the F distribution
• FINV inverse of the survival function of the F distribution
• FISHER Fisher transformation
• FISHERINV inverse of the Fisher transformation
• FORECAST estimates a future value according to existing values using simple linear regression
• FREQUENCY frequency table
• FTEST p-value for the two-tailed hypothesis test comparing the variances of two populations
• GAMMADIST probability density or cumulative distribution function of the gamma distribution
• GAMMAINV inverse of the cumulative gamma distribution
• GEOMDIST probability mass or cumulative distribution function of the geometric distribution
• GEOMEAN geometric mean
• GROWTH exponential growth prediction
• HARMEAN harmonic mean
• HYPGEOMDIST probability mass or cumulative distribution function of the hypergeometric distribution
• INTERCEPT the intercept of a linear regression line
• KURT unbiased estimate of the kurtosis of a data set
• KURTP population kurtosis of a data set
• LANDAU approximate probability density function of the Landau distribution
• LAPLACE probability density function of the Laplace distribution
• LARGE k-th largest value in a data set
• LEVERAGE calculate regression leverage
• LINEST multiple linear regression coefficients and statistics
• LKSTEST Lilliefors (Kolmogorov-Smirnov) Test of Normality
• LOGEST exponential least square fit
• LOGFIT logarithmic least square fit (using a trial and error method)
• LOGINV inverse of the cumulative distribution function of the lognormal distribution
• LOGISTIC probability density function of the logistic distribution
• LOGNORMDIST cumulative distribution function of the lognormal distribution
• LOGREG the logarithmic regression
• MAX largest value, with negative numbers considered smaller than positive numbers
• MAXA largest value, with negative numbers considered smaller than positive numbers
• MEDIAN median of a data set
• MIN smallest value, with negative numbers considered smaller than positive numbers
• MINA smallest value, with negative numbers considered smaller than positive numbers
• MODE first most common number in the dataset
• MODE.MULT most common numbers in the dataset
• NEGBINOMDIST probability mass function of the negative binomial distribution
• NORMDIST probability density or cumulative distribution function of a normal distribution
• NORMINV inverse of the cumulative distribution function of a normal distribution
• NORMSDIST cumulative distribution function of the standard normal distribution
• NORMSINV inverse of the cumulative distribution function of the standard normal distribution
• OWENT Owen's T function
• PARETO probability density function of the Pareto distribution
• PEARSON Pearson correlation coefficient of the paired set of data
• PERCENTILE determines the 100*k-th percentile of the given data points (Hyndman-Fan method 7: N-1 basis)
• PERCENTILE.EXC determines the 100*k-th percentile of the given data points (Hyndman-Fan method 6: N+1 basis)
• PERCENTRANK rank of a data point in a data set (Hyndman-Fan method 7: N-1 basis)
• PERCENTRANK.EXC rank of a data point in a data set (Hyndman-Fan method 6: N+1 basis)
• PERMUT number of k-permutations of a n-set
• PERMUTATIONA the number of permutations of y objects chosen from x objects with repetition allowed
• POISSON probability mass or cumulative distribution function of the Poisson distribution
• PROB probability of an interval for a discrete (and finite) probability distribution
• QUARTILE the k-th quartile of the data points (Hyndman-Fan method 7: N-1 basis)
• QUARTILE.EXC the k-th quartile of the data points (Hyndman-Fan method 6: N+1 basis)
• R.DBETA probability density function of the beta distribution
• R.DBINOM probability density function of the binomial distribution
• R.DCAUCHY probability density function of the Cauchy distribution
• R.DCHISQ probability density function of the chi-square distribution
• R.DEXP probability density function of the exponential distribution
• R.DF probability density function of the F distribution
• R.DGAMMA probability density function of the gamma distribution
• R.DGEOM probability density function of the geometric distribution
• R.DGUMBEL probability density function of the Gumbel distribution
• R.DHYPER probability density function of the hypergeometric distribution
• R.DLNORM probability density function of the log-normal distribution
• R.DNBINOM probability density function of the negative binomial distribution
• R.DNORM probability density function of the normal distribution
• R.DPOIS probability density function of the Poisson distribution
• R.DRAYLEIGH probability density function of the Rayleigh distribution
• R.DSNORM probability density function of the skew-normal distribution
• R.DST probability density function of the skew-t distribution
• R.DT probability density function of the Student t distribution
• R.DWEIBULL probability density function of the Weibull distribution
• R.PBETA cumulative distribution function of the beta distribution
• R.PBINOM cumulative distribution function of the binomial distribution
• R.PCAUCHY cumulative distribution function of the Cauchy distribution
• R.PCHISQ cumulative distribution function of the chi-square distribution
• R.PEXP cumulative distribution function of the exponential distribution
• R.PF cumulative distribution function of the F distribution
• R.PGAMMA cumulative distribution function of the gamma distribution
• R.PGEOM cumulative distribution function of the geometric distribution
• R.PGUMBEL cumulative distribution function of the Gumbel distribution
• R.PHYPER cumulative distribution function of the hypergeometric distribution
• R.PLNORM cumulative distribution function of the log-normal distribution
• R.PNBINOM cumulative distribution function of the negative binomial distribution
• R.PNORM cumulative distribution function of the normal distribution
• R.PPOIS cumulative distribution function of the Poisson distribution
• R.PRAYLEIGH cumulative distribution function of the Rayleigh distribution
• R.PSNORM cumulative distribution function of the skew-normal distribution
• R.PST cumulative distribution function of the skew-t distribution
• R.PT cumulative distribution function of the Student t distribution
• R.PTUKEY cumulative distribution function of the Studentized range distribution
• R.PWEIBULL cumulative distribution function of the Weibull distribution
• R.QBETA probability quantile function of the beta distribution
• R.QBINOM probability quantile function of the binomial distribution
• R.QCAUCHY probability quantile function of the Cauchy distribution
• R.QCHISQ probability quantile function of the chi-square distribution
• R.QEXP probability quantile function of the exponential distribution
• R.QF probability quantile function of the F distribution
• R.QGAMMA probability quantile function of the gamma distribution
• R.QGEOM probability quantile function of the geometric distribution
• R.QGUMBEL probability quantile function of the Gumbel distribution
• R.QHYPER probability quantile function of the hypergeometric distribution
• R.QLNORM probability quantile function of the log-normal distribution
• R.QNBINOM probability quantile function of the negative binomial distribution
• R.QNORM probability quantile function of the normal distribution
• R.QPOIS probability quantile function of the Poisson distribution
• R.QRAYLEIGH probability quantile function of the Rayleigh distribution
• R.QSNORM probability quantile function of the skew-normal distribution
• R.QST probability quantile function of the skew-t distribution
• R.QT probability quantile function of the Student t distribution
• R.QTUKEY probability quantile function of the Studentized range distribution
• R.QWEIBULL probability quantile function of the Weibull distribution
• RANK rank of a number in a list of numbers
• RANK.AVG rank of a number in a list of numbers
• RAYLEIGH probability density function of the Rayleigh distribution
• RAYLEIGHTAIL probability density function of the Rayleigh tail distribution
• RSQ square of the Pearson correlation coefficient of the paired set of data
• SFTEST Shapiro-Francia Test of Normality
• SKEW unbiased estimate for skewness of a distribution
• SKEWP population skewness of a data set
• SLOPE the slope of a linear regression line
• SMALL k-th smallest value in a data set
• SNORM.DIST.RANGE probability of the standard normal distribution over an interval
• SSMEDIAN median for grouped data
• STANDARDIZE z-score of a value
• STDEV sample standard deviation of the given sample
• STDEVA sample standard deviation of the given sample
• STDEVP population standard deviation of the given population
• STDEVPA population standard deviation of an entire population
• STEYX standard error of the predicted y-value in the regression
• SUBTOTAL the subtotal of the given list of arguments
• TDIST survival function of the Student t-distribution
• TINV two tailed inverse of the Student t-distribution
• TREND estimates future values of a given data set using a least squares approximation
• TRIMMEAN mean of the interior of a data set
• TTEST p-value for a hypothesis test comparing the means of two populations using the Student t-distribution
• VAR sample variance of the given sample
• VARA sample variance of the given sample
• VARP variance of an entire population
• VARPA variance of an entire population
• WEIBULL probability density or cumulative distribution function of the Weibull distribution
• ZTEST the probability of observing a sample mean as large as or larger than the mean of the given sample

### Arguments

x: array of sample values

### Description

This function returns an array with the first row giving the p-value of the Anderson-Darling Test, the second row the test statistic of the test, and the third the number of observations in the sample.

### Note

If there are less than 8 sample values, ADTEST returns #VALUE!

## AVEDEV

AVEDEV average of the absolute deviations of a data set

### Synopsis

AVEDEV(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

## AVERAGE

AVERAGE average of all the numeric values and cells

### Synopsis

AVERAGE(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

SUM, COUNT.

## AVERAGEA

AVERAGEA average of all the values and cells

### Synopsis

AVERAGEA(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Microsoft Excel Compatibility

This function is Excel compatible.

## BERNOULLI

BERNOULLI probability mass function of a Bernoulli distribution

BERNOULLI(k,p)

### Arguments

k: integer

p: probability of success

### Note

If k != 0 and k != 1 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error.

## BETA.DIST

BETA.DIST cumulative distribution function of the beta distribution

### Synopsis

BETA.DIST(x,alpha,beta,cumulative,a,b)

### Arguments

x: number

alpha: scale parameter

beta: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

a: optional lower bound, defaults to 0

b: optional upper bound, defaults to 1

### Note

If x < a or x > b this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error. If a >= b this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

BETADIST cumulative distribution function of the beta distribution

### Arguments

x: number

alpha: scale parameter

beta: scale parameter

a: optional lower bound, defaults to 0

b: optional upper bound, defaults to 1

### Note

If x < a or x > b this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error. If a >= b this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## BETAINV

BETAINV inverse of the cumulative distribution function of the beta distribution

### Synopsis

BETAINV(p,alpha,beta,a,b)

### Arguments

p: probability

alpha: scale parameter

beta: scale parameter

a: optional lower bound, defaults to 0

b: optional upper bound, defaults to 1

### Note

If p < 0 or p > 1 this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error. If a >= b this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## BINOM.DIST.RANGE

BINOM.DIST.RANGE probability of the binomial distribution over an interval

### Synopsis

BINOM.DIST.RANGE(trials,p,start,end)

### Arguments

trials: number of trials

p: probability of success in each trial

start: start of the interval

end: end of the interval, defaults to start

### Note

If start, end or trials are non-integer they are truncated. If trials < 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error. If start > end this function returns 0.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## BINOMDIST

BINOMDIST probability mass or cumulative distribution function of the binomial distribution

### Synopsis

BINOMDIST(n,trials,p,cumulative)

### Arguments

n: number of successes

trials: number of trials

p: probability of success in each trial

cumulative: whether to evaluate the mass function or the cumulative distribution function

### Note

If n or trials are non-integer they are truncated. If n < 0 or trials < 0 this function returns a #NUM! error. If n > trials this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## CAUCHY

CAUCHY probability density or cumulative distribution function of the Cauchy, Lorentz or Breit-Wigner distribution

### Synopsis

CAUCHY(x,a,cumulative)

### Arguments

x: number

a: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

### Note

If a < 0 this function returns a #NUM! error. If cumulative is neither TRUE nor FALSE this function returns a #VALUE! error.

## CHIDIST

CHIDIST survival function of the chi-squared distribution

CHIDIST(x,dof)

### Arguments

x: number

dof: number of degrees of freedom

### Description

The survival function is 1 minus the cumulative distribution function.

### Note

If dof is non-integer it is truncated. If dof < 1 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

CHIDIST(x,dof) is the OpenFormula function LEGACY.CHIDIST(x,dof).

## CHIINV

CHIINV inverse of the survival function of the chi-squared distribution

CHIINV(p,dof)

### Arguments

p: probability

dof: number of degrees of freedom

### Description

The survival function is 1 minus the cumulative distribution function.

### Note

If p < 0 or p > 1 or dof < 1 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

CHIINV(p,dof) is the OpenFormula function LEGACY.CHIDIST(p,dof).

## CHITEST

CHITEST p value of the Goodness of Fit Test

### Synopsis

CHITEST(actual_range,theoretical_range)

### Arguments

actual_range: observed data

theoretical_range: expected values

### Note

If the actual range is not an n by 1 or 1 by n range, but an n by m range, then CHITEST uses (n-1) times (m-1) as degrees of freedom. This is useful if the expected values were calculated from the observed value in a test of independence or test of homogeneity.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

CHITEST is the OpenFormula function LEGACY.CHITEST.

## CONFIDENCE

CONFIDENCE margin of error of a confidence interval for the population mean

### Synopsis

CONFIDENCE(alpha,stddev,size)

### Arguments

alpha: significance level

stddev: population standard deviation

size: sample size

### Note

This function requires the usually unknown population standard deviation. If size is non-integer it is truncated. If size < 0 this function returns a #NUM! error. If size is 0 this function returns a #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## CONFIDENCE.T

CONFIDENCE.T margin of error of a confidence interval for the population mean using the Student's t-distribution

### Synopsis

CONFIDENCE.T(alpha,stddev,size)

### Arguments

alpha: significance level

stddev: sample standard deviation

size: sample size

### Note

If stddev < 0 or = 0 this function returns a #NUM! error. If size is non-integer it is truncated. If size < 1 this function returns a #NUM! error. If size is 1 this function returns a #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## CORREL

CORREL Pearson correlation coefficient of two data sets

### Synopsis

CORREL(array1,array2)

### Arguments

array1: first data set

array2: second data set

### Description

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## COUNT

COUNT total number of integer or floating point arguments passed

### Synopsis

COUNT(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

## COUNTA

COUNTA number of arguments passed not including empty cells

### Synopsis

COUNTA(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

## COVAR

COVAR covariance of two data sets

### Synopsis

COVAR(array1,array2)

### Arguments

array1: first data set

array2: set data set

### Description

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## COVARIANCE.S

COVARIANCE.S sample covariance of two data sets

### Synopsis

COVARIANCE.S(array1,array2)

### Arguments

array1: first data set

array2: set data set

### Description

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## CRITBINOM

CRITBINOM right-tailed critical value of the binomial distribution

### Synopsis

CRITBINOM(trials,p,alpha)

### Arguments

trials: number of trials

p: probability of success in each trial

alpha: significance level (area of the tail)

### Note

If trials is a non-integer it is truncated. If trials < 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error. If alpha < 0 or alpha > 1 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## CRONBACH

CRONBACH Cronbach's alpha

### Synopsis

CRONBACH(ref1,ref2,…)

### Arguments

ref1: first data set

ref2: second data set

VAR.

## CVMTEST

CVMTEST Cramér-von Mises Test of Normality

CVMTEST(x)

### Arguments

x: array of sample values

### Description

This function returns an array with the first row giving the p-value of the Cramér-von Mises Test, the second row the test statistic of the test, and the third the number of observations in the sample.

### Note

If there are less than 8 sample values, CVMTEST returns #VALUE!

## DEVSQ

DEVSQ sum of squares of deviations of a data set

### Synopsis

DEVSQ(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## EXPONDIST

EXPONDIST probability density or cumulative distribution function of the exponential distribution

### Synopsis

EXPONDIST(x,y,cumulative)

### Arguments

x: number

y: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

### Description

If cumulative is false it will return: y * exp (-y*x), otherwise it will return 1 - exp (-y*x).

### Note

If x < 0 or y <= 0 this will return an error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## EXPPOWDIST

EXPPOWDIST the probability density function of the Exponential Power distribution

### Synopsis

EXPPOWDIST(x,a,b)

### Arguments

x: number

a: scale parameter

b: scale parameter

### Description

This distribution has been recommended for lifetime analysis when a U-shaped hazard function is desired. This corresponds to rapid failure once the product starts to wear out after a period of steady or even improving reliability.

## FDIST

FDIST survival function of the F distribution

### Synopsis

FDIST(x,dof_of_num,dof_of_denom)

### Arguments

x: number

dof_of_num: numerator degrees of freedom

dof_of_denom: denominator degrees of freedom

### Description

The survival function is 1 minus the cumulative distribution function.

### Note

If x < 0 this function returns a #NUM! error. If dof_of_num < 1 or dof_of_denom < 1, this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

FDIST is the OpenFormula function LEGACY.FDIST.

FINV.

## FINV

FINV inverse of the survival function of the F distribution

### Synopsis

FINV(p,dof_of_num,dof_of_denom)

### Arguments

p: probability

dof_of_num: numerator degrees of freedom

dof_of_denom: denominator degrees of freedom

### Description

The survival function is 1 minus the cumulative distribution function.

### Note

If p < 0 or p > 1 this function returns a #NUM! error. If dof_of_num < 1 or dof_of_denom < 1 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

FINV is the OpenFormula function LEGACY.FINV.

## FISHER

FISHER Fisher transformation

FISHER(x)

x: number

### Note

If x is not a number, this function returns a #VALUE! error. If x <= -1 or x >= 1, this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## FISHERINV

FISHERINV inverse of the Fisher transformation

FISHERINV(x)

x: number

### Note

If x is a non-number this function returns a #VALUE! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## FORECAST

FORECAST estimates a future value according to existing values using simple linear regression

### Synopsis

FORECAST(x,known_ys,known_xs)

### Arguments

x: x-value whose matching y-value should be forecast

known_ys: known y-values

known_xs: known x-values

### Description

This function estimates a future value according to existing values using simple linear regression.

### Note

If known_xs or known_ys contains no data entries or different number of data entries, this function returns a #N/A error. If the variance of the known_xs is zero, this function returns a #DIV/0 error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## FREQUENCY

FREQUENCY frequency table

### Synopsis

FREQUENCY(data_array,bins_array)

### Arguments

data_array: data values

bins_array: array of cutoff values

### Description

The results are given as an array.

If the bins_array is empty, this function returns the number of data points in data_array.

### Microsoft Excel Compatibility

This function is Excel compatible.

## FTEST

FTEST p-value for the two-tailed hypothesis test comparing the variances of two populations

### Synopsis

FTEST(array1,array2)

### Arguments

array1: sample from the first population

array2: sample from the second population

### Microsoft Excel Compatibility

This function is Excel compatible.

GAMMADIST probability density or cumulative distribution function of the gamma distribution

### Arguments

x: number

alpha: scale parameter

beta: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

### Note

If x < 0 this function returns a #NUM! error. If alpha <= 0 or beta <= 0, this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## GAMMAINV

GAMMAINV inverse of the cumulative gamma distribution

### Synopsis

GAMMAINV(p,alpha,beta)

### Arguments

p: probability

alpha: scale parameter

beta: scale parameter

### Note

If p < 0 or p > 1 this function returns a #NUM! error. If alpha <= 0 or beta <= 0 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## GEOMDIST

GEOMDIST probability mass or cumulative distribution function of the geometric distribution

### Synopsis

GEOMDIST(k,p,cumulative)

### Arguments

k: number of trials

p: probability of success in any trial

cumulative: whether to evaluate the mass function or the cumulative distribution function

### Note

If k < 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error. If cumulative is neither TRUE nor FALSE this function returns a #VALUE! error.

## GEOMEAN

GEOMEAN geometric mean

### Synopsis

GEOMEAN(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

The geometric mean is equal to the Nth root of the product of the N values.

### Microsoft Excel Compatibility

This function is Excel compatible.

## GROWTH

GROWTH exponential growth prediction

### Synopsis

GROWTH(known_ys,known_xs,new_xs,affine)

### Arguments

known_ys: known y-values

known_xs: known x-values; defaults to the array {1, 2, 3, …}

new_xs: x-values for which to estimate the y-values; defaults to known_xs

affine: if true, the model contains a constant term, defaults to true

### Description

GROWTH function applies the “least squares” method to fit an exponential curve to your data and predicts the exponential growth by using this curve.

GROWTH returns an array having one column and a row for each data point in new_xs.

### Note

If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

## HARMEAN

HARMEAN harmonic mean

### Synopsis

HARMEAN(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

The harmonic mean of N data points is N divided by the sum of the reciprocals of the data points).

### Microsoft Excel Compatibility

This function is Excel compatible.

## HYPGEOMDIST

HYPGEOMDIST probability mass or cumulative distribution function of the hypergeometric distribution

### Synopsis

HYPGEOMDIST(x,n,M,N,cumulative)

### Arguments

x: number of successes

n: sample size

M: number of possible successes in the population

N: population size

cumulative: whether to evaluate the mass function or the cumulative distribution function

### Note

If x,n,M or N is a non-integer it is truncated. If x,n,M or N < 0 this function returns a #NUM! error. If x > M or n > N this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## INTERCEPT

INTERCEPT the intercept of a linear regression line

### Synopsis

INTERCEPT(known_ys,known_xs)

### Arguments

known_ys: known y-values

known_xs: known x-values

### Note

If known_xs or known_ys contains no data entries or different number of data entries, this function returns a #N/A error. If the variance of the known_xs is zero, this function returns #DIV/0 error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## KURT

KURT unbiased estimate of the kurtosis of a data set

### Synopsis

KURT(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

### Note

This is only meaningful if the underlying distribution really has a fourth moment. The kurtosis is offset by three such that a normal distribution will have zero kurtosis. If fewer than four numbers are given or all of them are equal this function returns a #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## KURTP

KURTP population kurtosis of a data set

### Synopsis

KURTP(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

### Note

If fewer than two numbers are given or all of them are equal this function returns a #DIV/0! error.

## LANDAU

LANDAU approximate probability density function of the Landau distribution

LANDAU(x)

x: number

## LAPLACE

LAPLACE probability density function of the Laplace distribution

LAPLACE(x,a)

x: number

a: mean

## LARGE

LARGE k-th largest value in a data set

LARGE(data,k)

### Arguments

data: data set

k: which value to find

### Note

If data set is empty this function returns a #NUM! error. If k <= 0 or k is greater than the number of data items given this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## LEVERAGE

LEVERAGE calculate regression leverage

LEVERAGE(A)

A: a matrix

### Description

Returns the diagonal of A (A^T A)^-1 A^T as a column vector.

### Note

If the matrix is singular, #VALUE! is returned.

## LINEST

LINEST multiple linear regression coefficients and statistics

### Synopsis

LINEST(known_ys,known_xs,affine,stats)

### Arguments

known_ys: vector of values of dependent variable

known_xs: array of values of independent variables, defaults to a single vector {1,…,n}

affine: if true, the model contains a constant term, defaults to true

stats: if true, some additional statistics are provided, defaults to false

### Description

This function returns an array with the first row giving the regression coefficients for the independent variables x_m, x_(m-1),…,x_2, x_1 followed by the y-intercept if affine is true.

If stats is true, the second row contains the corresponding standard errors of the regression coefficients. In this case, the third row contains the R^2 value and the standard error for the predicted value. The fourth row contains the observed F value and its degrees of freedom. Finally, the fifth row contains the regression sum of squares and the residual sum of squares.

If affine is false, R^2 is the uncentered version of the coefficient of determination; that is the proportion of the sum of squares explained by the model.

### Note

If the length of known_ys does not match the corresponding length of known_xs, this function returns a #NUM! error.

## LKSTEST

LKSTEST Lilliefors (Kolmogorov-Smirnov) Test of Normality

LKSTEST(x)

### Arguments

x: array of sample values

### Description

This function returns an array with the first row giving the p-value of the Lilliefors (Kolmogorov-Smirnov) Test, the second row the test statistic of the test, and the third the number of observations in the sample.

### Note

If there are less than 5 sample values, LKSTEST returns #VALUE!

## LOGEST

LOGEST exponential least square fit

### Synopsis

LOGEST(known_ys,known_xs,affine,stat)

### Arguments

known_ys: known y-values

known_xs: known x-values; default to an array {1, 2, 3, …}

affine: if true, the model contains a constant term, defaults to true

stat: if true, extra statistical information will be returned; defaults to FALSE

### Description

LOGEST function applies the “least squares” method to fit an exponential curve of the form y = b * m{1}^x{1} * m{2}^x{2}... to your data.

LOGEST returns an array { m{n},m{n-1}, ...,m{1},b }.

### Note

Extra statistical information is written below the regression line coefficients in the result array. Extra statistical information consists of four rows of data. In the first row the standard error values for the coefficients m1, (m2, ...), b are represented. The second row contains the square of R and the standard error for the y estimate. The third row contains the F-observed value and the degrees of freedom. The last row contains the regression sum of squares and the residual sum of squares. If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

## LOGFIT

LOGFIT logarithmic least square fit (using a trial and error method)

### Synopsis

LOGFIT(known_ys,known_xs)

### Arguments

known_ys: known y-values

known_xs: known x-values

### Description

LOGFIT function applies the “least squares” method to fit the logarithmic equation y = a + b * ln(sign * (x - c)) , sign = +1 or -1 to your data. The graph of the equation is a logarithmic curve moved horizontally by c and possibly mirrored across the y-axis (if sign = -1).

LOGFIT returns an array having five columns and one row. `Sign' is given in the first column, `a', `b', and `c' are given in columns 2 to 4. Column 5 holds the sum of squared residuals.

### Note

An error is returned when there are less than 3 different x's or y's, or when the shape of the point cloud is too different from a ``logarithmic'' one. You can use the above formula = a + b * ln(sign * (x - c)) or rearrange it to = (exp((y - a) / b)) / sign + c to compute unknown y's or x's, respectively. This is non-linear fitting by trial-and-error. The accuracy of `c' is: width of x-range -> rounded to the next smaller (10^integer), times 0.000001. There might be cases in which the returned fit is not the best possible.

LOGINV inverse of the cumulative distribution function of the lognormal distribution

### Arguments

p: probability

mean: mean

stddev: standard deviation

### Note

If p < 0 or p > 1 or stddev <= 0 this function returns #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## LOGISTIC

LOGISTIC probability density function of the logistic distribution

LOGISTIC(x,a)

### Arguments

x: number

a: scale parameter

## LOGNORMDIST

LOGNORMDIST cumulative distribution function of the lognormal distribution

### Synopsis

LOGNORMDIST(x,mean,stddev)

### Arguments

x: number

mean: mean

stddev: standard deviation

### Note

If stddev = 0 LOGNORMDIST returns a #DIV/0! error. If x <= 0, mean < 0 or stddev <= 0 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## LOGREG

LOGREG the logarithmic regression

### Synopsis

LOGREG(known_ys,known_xs,affine,stat)

### Arguments

known_ys: known y-values

known_xs: known x-values; defaults to the array {1, 2, 3, …}

affine: if true, the model contains a constant term, defaults to true

stat: if true, extra statistical information will be returned; defaults to FALSE

### Description

LOGREG function transforms your x's to z=ln(x) and applies the “least squares” method to fit the linear equation y = m * z + b to your y's and z's --- equivalent to fitting the equation y = m * ln(x) + b to y's and x's. LOGREG returns an array having two columns and one row. m is given in the first column and b in the second.

Any extra statistical information is written below m and b in the result array. This extra statistical information consists of four rows of data: In the first row the standard error values for the coefficients m, b are given. The second row contains the square of R and the standard error for the y estimate. The third row contains the F-observed value and the degrees of freedom. The last row contains the regression sum of squares and the residual sum of squares. The default of stat is FALSE.

### Note

If known_ys and known_xs have unequal number of data points, this function returns a #NUM! error.

## MAX

MAX largest value, with negative numbers considered smaller than positive numbers

### Synopsis

MAX(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

MIN, ABS.

## MAXA

MAXA largest value, with negative numbers considered smaller than positive numbers

### Synopsis

MAXA(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Microsoft Excel Compatibility

This function is Excel compatible.

MAX, MINA.

## MEDIAN

MEDIAN median of a data set

### Synopsis

MEDIAN(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

### Note

If even numbers are given MEDIAN returns the average of the two numbers in the center.

### Microsoft Excel Compatibility

This function is Excel compatible.

## MIN

MIN smallest value, with negative numbers considered smaller than positive numbers

### Synopsis

MIN(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

MAX, ABS.

## MINA

MINA smallest value, with negative numbers considered smaller than positive numbers

### Synopsis

MINA(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Microsoft Excel Compatibility

This function is Excel compatible.

MIN, MAXA.

## MODE

MODE first most common number in the dataset

### Synopsis

MODE(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

If the data set does not contain any duplicates this function returns a #N/A error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## MODE.MULT

MODE.MULT most common numbers in the dataset

### Synopsis

MODE.MULT(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

If the data set does not contain any duplicates this function returns a #N/A error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## NEGBINOMDIST

NEGBINOMDIST probability mass function of the negative binomial distribution

### Synopsis

NEGBINOMDIST(f,t,p)

### Arguments

f: number of failures

t: threshold number of successes

p: probability of a success

### Note

If f or t is a non-integer it is truncated. If (f + t -1) <= 0 this function returns a #NUM! error. If p < 0 or p > 1 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## NORMDIST

NORMDIST probability density or cumulative distribution function of a normal distribution

### Synopsis

NORMDIST(x,mean,stddev,cumulative)

### Arguments

x: number

mean: mean of the distribution

stddev: standard deviation of the distribution

cumulative: whether to evaluate the density function or the cumulative distribution function

### Note

If stddev is 0 this function returns a #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## NORMINV

NORMINV inverse of the cumulative distribution function of a normal distribution

### Synopsis

NORMINV(p,mean,stddev)

### Arguments

p: probability

mean: mean of the distribution

stddev: standard deviation of the distribution

### Note

If p < 0 or p > 1 or stddev <= 0 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## NORMSDIST

NORMSDIST cumulative distribution function of the standard normal distribution

NORMSDIST(x)

x: number

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

NORMSDIST is the OpenFormula function LEGACY.NORMSDIST.

## NORMSINV

NORMSINV inverse of the cumulative distribution function of the standard normal distribution

NORMSINV(p)

### Arguments

p: given probability

### Note

If p < 0 or p > 1 this function returns #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

NORMSINV is the OpenFormula function LEGACY.NORMSINV.

## OWENT

OWENT Owen's T function

OWENT(h,a)

h: number

a: number

## PARETO

PARETO probability density function of the Pareto distribution

PARETO(x,a,b)

### Arguments

x: number

a: exponent

b: scale parameter

## PEARSON

PEARSON Pearson correlation coefficient of the paired set of data

### Synopsis

PEARSON(array1,array2)

### Arguments

array1: first component values

array2: second component values

### Description

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## PERCENTILE

PERCENTILE determines the 100*k-th percentile of the given data points (Hyndman-Fan method 7: N-1 basis)

### Synopsis

PERCENTILE(array,k)

### Arguments

array: data points

k: which percentile to calculate

### Note

If array is empty, this function returns a #NUM! error. If k < 0 or k > 1, this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## PERCENTILE.EXC

PERCENTILE.EXC determines the 100*k-th percentile of the given data points (Hyndman-Fan method 6: N+1 basis)

### Synopsis

PERCENTILE.EXC(array,k)

### Arguments

array: data points

k: which percentile to calculate

### Note

If array is empty, this function returns a #NUM! error. If k < 0 or k > 1, this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## PERCENTRANK

PERCENTRANK rank of a data point in a data set (Hyndman-Fan method 7: N-1 basis)

### Synopsis

PERCENTRANK(array,x,significance)

### Arguments

array: range of numeric values

x: data point to be ranked

significance: number of significant digits, defaults to 3

### Note

If array contains no data points, this function returns a #NUM! error. If significance is less than one, this function returns a #NUM! error. If x exceeds the largest value or is less than the smallest value in array, this function returns an #N/A error. If x does not match any of the values in array or x matches more than once, this function interpolates the returned value.

## PERCENTRANK.EXC

PERCENTRANK.EXC rank of a data point in a data set (Hyndman-Fan method 6: N+1 basis)

### Synopsis

PERCENTRANK.EXC(array,x,significance)

### Arguments

array: range of numeric values

x: data point to be ranked

significance: number of significant digits, defaults to 3

### Note

If array contains no data points, this function returns a #NUM! error. If significance is less than one, this function returns a #NUM! error. If x exceeds the largest value or is less than the smallest value in array, this function returns an #N/A error. If x does not match any of the values in array or x matches more than once, this function interpolates the returned value.

## PERMUT

PERMUT number of k-permutations of a n-set

PERMUT(n,k)

### Arguments

n: size of the base set

k: number of elements in each permutation

### Note

If n = 0 this function returns a #NUM! error. If n < k this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## PERMUTATIONA

PERMUTATIONA the number of permutations of y objects chosen from x objects with repetition allowed

### Synopsis

PERMUTATIONA(x,y)

### Arguments

x: total number of objects

y: number of selected objects

### Note

If both x and y equal 0, PERMUTATIONA returns 1. If x < 0 or y < 0, PERMUTATIONA returns #NUM! If x or y are not integers, they are truncated.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.

## POISSON

POISSON probability mass or cumulative distribution function of the Poisson distribution

### Synopsis

POISSON(x,mean,cumulative)

### Arguments

x: number of events

mean: mean of the distribution

cumulative: whether to evaluate the mass function or the cumulative distribution function

### Note

If x is a non-integer it is truncated. If x < 0 this function returns a #NUM! error. If mean <= 0 POISSON returns the #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## PROB

PROB probability of an interval for a discrete (and finite) probability distribution

### Synopsis

PROB(x_range,prob_range,lower_limit,upper_limit)

### Arguments

x_range: possible values

prob_range: probabilities of the corresponding values

lower_limit: lower interval limit

upper_limit: upper interval limit, defaults to lower_limit

### Note

If the sum of the probabilities in prob_range is not equal to 1 this function returns a #NUM! error. If any value in prob_range is <=0 or > 1, this function returns a #NUM! error. If x_range and prob_range contain a different number of data entries, this function returns a #N/A error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## QUARTILE

QUARTILE the k-th quartile of the data points (Hyndman-Fan method 7: N-1 basis)

### Synopsis

QUARTILE(array,quart)

### Arguments

array: data points

quart: a number from 0 to 4, indicating which quartile to calculate

### Note

If array is empty, this function returns a #NUM! error. If quart < 0 or quart > 4, this function returns a #NUM! error. If quart = 0, the smallest value of array to be returned. If quart is not an integer, it is truncated.

### Microsoft Excel Compatibility

This function is Excel compatible.

## QUARTILE.EXC

QUARTILE.EXC the k-th quartile of the data points (Hyndman-Fan method 6: N+1 basis)

### Synopsis

QUARTILE.EXC(array,quart)

### Arguments

array: data points

quart: a number from 1 to 3, indicating which quartile to calculate

### Note

If array is empty, this function returns a #NUM! error. If quart < 0 or quart > 4, this function returns a #NUM! error. If quart = 0, the smallest value of array to be returned. If quart is not an integer, it is truncated.

### Microsoft Excel Compatibility

This function is Excel compatible.

## R.DBETA

R.DBETA probability density function of the beta distribution

### Synopsis

R.DBETA(x,a,b,give_log)

### Arguments

x: observation

a: the first shape parameter of the distribution

b: the second scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the beta distribution.

## R.DBINOM

R.DBINOM probability density function of the binomial distribution

### Synopsis

R.DBINOM(x,n,psuc,give_log)

### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the binomial distribution.

## R.DCAUCHY

R.DCAUCHY probability density function of the Cauchy distribution

### Synopsis

R.DCAUCHY(x,location,scale,give_log)

### Arguments

x: observation

location: the center of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the Cauchy distribution.

## R.DCHISQ

R.DCHISQ probability density function of the chi-square distribution

### Synopsis

R.DCHISQ(x,df,give_log)

### Arguments

x: observation

df: the number of degrees of freedom of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the chi-square distribution.

### OpenDocument Format (ODF) Compatibility

A two argument invocation R.DCHISQ(x,df) is exported to OpenFormula as CHISQDIST(x,df,FALSE()).

## R.DEXP

R.DEXP probability density function of the exponential distribution

### Synopsis

R.DEXP(x,scale,give_log)

### Arguments

x: observation

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the exponential distribution.

## R.DF

R.DF probability density function of the F distribution

### Synopsis

R.DF(x,n1,n2,give_log)

### Arguments

x: observation

n1: the first number of degrees of freedom of the distribution

n2: the second number of degrees of freedom of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the F distribution.

R.PF, R.QF.

## R.DGAMMA

R.DGAMMA probability density function of the gamma distribution

### Synopsis

R.DGAMMA(x,shape,scale,give_log)

### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the gamma distribution.

## R.DGEOM

R.DGEOM probability density function of the geometric distribution

### Synopsis

R.DGEOM(x,psuc,give_log)

### Arguments

x: observation

psuc: the probability of success in each trial

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the geometric distribution.

## R.DGUMBEL

R.DGUMBEL probability density function of the Gumbel distribution

### Synopsis

R.DGUMBEL(x,mu,beta,give_log)

### Arguments

x: observation

mu: the location parameter of freedom of the distribution

beta: the scale parameter of freedom of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the Gumbel distribution.

## R.DHYPER

R.DHYPER probability density function of the hypergeometric distribution

### Synopsis

R.DHYPER(x,r,b,n,give_log)

### Arguments

x: observation

r: the number of red balls

b: the number of black balls

n: the number of balls drawn

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the hypergeometric distribution.

## R.DLNORM

R.DLNORM probability density function of the log-normal distribution

### Synopsis

R.DLNORM(x,logmean,logsd,give_log)

### Arguments

x: observation

logmean: mean of the underlying normal distribution

logsd: standard deviation of the underlying normal distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the log-normal distribution.

## R.DNBINOM

R.DNBINOM probability density function of the negative binomial distribution

### Synopsis

R.DNBINOM(x,n,psuc,give_log)

### Arguments

x: observation (number of failures)

n: required number of successes

psuc: the probability of success in each trial

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the negative binomial distribution.

## R.DNORM

R.DNORM probability density function of the normal distribution

### Synopsis

R.DNORM(x,mu,sigma,give_log)

### Arguments

x: observation

mu: mean of the distribution

sigma: standard deviation of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the normal distribution.

## R.DPOIS

R.DPOIS probability density function of the Poisson distribution

### Synopsis

R.DPOIS(x,lambda,give_log)

### Arguments

x: observation

lambda: the mean of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the Poisson distribution.

## R.DRAYLEIGH

R.DRAYLEIGH probability density function of the Rayleigh distribution

### Synopsis

R.DRAYLEIGH(x,scale,give_log)

### Arguments

x: observation

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the Rayleigh distribution.

## R.DSNORM

R.DSNORM probability density function of the skew-normal distribution

### Synopsis

R.DSNORM(x,shape,location,scale,give_log)

### Arguments

x: observation

shape: the shape parameter of the distribution

location: the location parameter of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the skew-normal distribution.

## R.DST

R.DST probability density function of the skew-t distribution

### Synopsis

R.DST(x,n,shape,give_log)

### Arguments

x: observation

n: the number of degrees of freedom of the distribution

shape: the shape parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the skew-t distribution.

## R.DT

R.DT probability density function of the Student t distribution

### Synopsis

R.DT(x,n,give_log)

### Arguments

x: observation

n: the number of degrees of freedom of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the Student t distribution.

R.PT, R.QT.

## R.DWEIBULL

R.DWEIBULL probability density function of the Weibull distribution

### Synopsis

R.DWEIBULL(x,shape,scale,give_log)

### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

give_log: if true, log of the result will be returned instead

### Description

This function returns the probability density function of the Weibull distribution.

## R.PBETA

R.PBETA cumulative distribution function of the beta distribution

### Synopsis

R.PBETA(x,a,b,lower_tail,log_p)

### Arguments

x: observation

a: the first shape parameter of the distribution

b: the second scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the beta distribution.

## R.PBINOM

R.PBINOM cumulative distribution function of the binomial distribution

### Synopsis

R.PBINOM(x,n,psuc,lower_tail,log_p)

### Arguments

x: observation

n: the number of trials

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the binomial distribution.

## R.PCAUCHY

R.PCAUCHY cumulative distribution function of the Cauchy distribution

### Synopsis

R.PCAUCHY(x,location,scale,lower_tail,log_p)

### Arguments

x: observation

location: the center of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Cauchy distribution.

## R.PCHISQ

R.PCHISQ cumulative distribution function of the chi-square distribution

### Synopsis

R.PCHISQ(x,df,lower_tail,log_p)

### Arguments

x: observation

df: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the chi-square distribution.

### OpenDocument Format (ODF) Compatibility

A two argument invocation R.PCHISQ(x,df) is exported to OpenFormula as CHISQDIST(x,df).

## R.PEXP

R.PEXP cumulative distribution function of the exponential distribution

### Synopsis

R.PEXP(x,scale,lower_tail,log_p)

### Arguments

x: observation

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the exponential distribution.

## R.PF

R.PF cumulative distribution function of the F distribution

### Synopsis

R.PF(x,n1,n2,lower_tail,log_p)

### Arguments

x: observation

n1: the first number of degrees of freedom of the distribution

n2: the second number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the F distribution.

R.DF, R.QF.

## R.PGAMMA

R.PGAMMA cumulative distribution function of the gamma distribution

### Synopsis

R.PGAMMA(x,shape,scale,lower_tail,log_p)

### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the gamma distribution.

## R.PGEOM

R.PGEOM cumulative distribution function of the geometric distribution

### Synopsis

R.PGEOM(x,psuc,lower_tail,log_p)

### Arguments

x: observation

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the geometric distribution.

## R.PGUMBEL

R.PGUMBEL cumulative distribution function of the Gumbel distribution

### Synopsis

R.PGUMBEL(x,mu,beta,lower_tail,log_p)

### Arguments

x: observation

mu: the location parameter of freedom of the distribution

beta: the scale parameter of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Gumbel distribution.

## R.PHYPER

R.PHYPER cumulative distribution function of the hypergeometric distribution

### Synopsis

R.PHYPER(x,r,b,n,lower_tail,log_p)

### Arguments

x: observation

r: the number of red balls

b: the number of black balls

n: the number of balls drawn

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the hypergeometric distribution.

## R.PLNORM

R.PLNORM cumulative distribution function of the log-normal distribution

### Synopsis

R.PLNORM(x,logmean,logsd,lower_tail,log_p)

### Arguments

x: observation

logmean: mean of the underlying normal distribution

logsd: standard deviation of the underlying normal distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the log-normal distribution.

## R.PNBINOM

R.PNBINOM cumulative distribution function of the negative binomial distribution

### Synopsis

R.PNBINOM(x,n,psuc,lower_tail,log_p)

### Arguments

x: observation (number of failures)

n: required number of successes

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the negative binomial distribution.

## R.PNORM

R.PNORM cumulative distribution function of the normal distribution

### Synopsis

R.PNORM(x,mu,sigma,lower_tail,log_p)

### Arguments

x: observation

mu: mean of the distribution

sigma: standard deviation of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the normal distribution.

## R.PPOIS

R.PPOIS cumulative distribution function of the Poisson distribution

### Synopsis

R.PPOIS(x,lambda,lower_tail,log_p)

### Arguments

x: observation

lambda: the mean of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Poisson distribution.

## R.PRAYLEIGH

R.PRAYLEIGH cumulative distribution function of the Rayleigh distribution

### Synopsis

R.PRAYLEIGH(x,scale,lower_tail,log_p)

### Arguments

x: observation

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Rayleigh distribution.

## R.PSNORM

R.PSNORM cumulative distribution function of the skew-normal distribution

### Synopsis

R.PSNORM(x,shape,location,scale,lower_tail,log_p)

### Arguments

x: observation

shape: the shape parameter of the distribution

location: the location parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the skew-normal distribution.

## R.PST

R.PST cumulative distribution function of the skew-t distribution

### Synopsis

R.PST(x,n,shape,lower_tail,log_p)

### Arguments

x: observation

n: the number of degrees of freedom of the distribution

shape: the shape parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the skew-t distribution.

## R.PT

R.PT cumulative distribution function of the Student t distribution

### Synopsis

R.PT(x,n,lower_tail,log_p)

### Arguments

x: observation

n: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Student t distribution.

R.DT, R.QT.

## R.PTUKEY

R.PTUKEY cumulative distribution function of the Studentized range distribution

### Synopsis

R.PTUKEY(x,nmeans,df,nranges,lower_tail,log_p)

### Arguments

x: observation

nmeans: the number of means

df: the number of degrees of freedom of the distribution

nranges: the number of ranges; default is 1

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Studentized range distribution.

## R.PWEIBULL

R.PWEIBULL cumulative distribution function of the Weibull distribution

### Synopsis

R.PWEIBULL(x,shape,scale,lower_tail,log_p)

### Arguments

x: observation

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the cumulative distribution function of the Weibull distribution.

## R.QBETA

R.QBETA probability quantile function of the beta distribution

### Synopsis

R.QBETA(p,a,b,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

a: the first shape parameter of the distribution

b: the second scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the beta distribution.

## R.QBINOM

R.QBINOM probability quantile function of the binomial distribution

### Synopsis

R.QBINOM(p,n,psuc,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

n: the number of trials

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the binomial distribution.

## R.QCAUCHY

R.QCAUCHY probability quantile function of the Cauchy distribution

### Synopsis

R.QCAUCHY(p,location,scale,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

location: the center of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Cauchy distribution.

## R.QCHISQ

R.QCHISQ probability quantile function of the chi-square distribution

### Synopsis

R.QCHISQ(p,df,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

df: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the chi-square distribution.

### OpenDocument Format (ODF) Compatibility

A two argument invocation R.QCHISQ(p,df) is exported to OpenFormula as CHISQINV(p,df).

## R.QEXP

R.QEXP probability quantile function of the exponential distribution

### Synopsis

R.QEXP(p,scale,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the exponential distribution.

## R.QF

R.QF probability quantile function of the F distribution

### Synopsis

R.QF(p,n1,n2,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

n1: the first number of degrees of freedom of the distribution

n2: the second number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the F distribution.

R.DF, R.PF.

## R.QGAMMA

R.QGAMMA probability quantile function of the gamma distribution

### Synopsis

R.QGAMMA(p,shape,scale,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the gamma distribution.

## R.QGEOM

R.QGEOM probability quantile function of the geometric distribution

### Synopsis

R.QGEOM(p,psuc,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the geometric distribution.

## R.QGUMBEL

R.QGUMBEL probability quantile function of the Gumbel distribution

### Synopsis

R.QGUMBEL(p,mu,beta,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

mu: the location parameter of freedom of the distribution

beta: the scale parameter of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Gumbel distribution.

## R.QHYPER

R.QHYPER probability quantile function of the hypergeometric distribution

### Synopsis

R.QHYPER(p,r,b,n,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

r: the number of red balls

b: the number of black balls

n: the number of balls drawn

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the hypergeometric distribution.

## R.QLNORM

R.QLNORM probability quantile function of the log-normal distribution

### Synopsis

R.QLNORM(p,logmean,logsd,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

logmean: mean of the underlying normal distribution

logsd: standard deviation of the underlying normal distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the log-normal distribution.

## R.QNBINOM

R.QNBINOM probability quantile function of the negative binomial distribution

### Synopsis

R.QNBINOM(p,n,psuc,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

n: required number of successes

psuc: the probability of success in each trial

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the negative binomial distribution.

## R.QNORM

R.QNORM probability quantile function of the normal distribution

### Synopsis

R.QNORM(p,mu,sigma,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

mu: mean of the distribution

sigma: standard deviation of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the normal distribution.

## R.QPOIS

R.QPOIS probability quantile function of the Poisson distribution

### Synopsis

R.QPOIS(p,lambda,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

lambda: the mean of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Poisson distribution.

## R.QRAYLEIGH

R.QRAYLEIGH probability quantile function of the Rayleigh distribution

### Synopsis

R.QRAYLEIGH(p,scale,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Rayleigh distribution.

## R.QSNORM

R.QSNORM probability quantile function of the skew-normal distribution

### Synopsis

R.QSNORM(p,shape,location,scale,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

shape: the shape parameter of the distribution

location: the location parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the skew-normal distribution.

## R.QST

R.QST probability quantile function of the skew-t distribution

### Synopsis

R.QST(p,n,shape,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

n: the number of degrees of freedom of the distribution

shape: the shape parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the skew-t distribution.

## R.QT

R.QT probability quantile function of the Student t distribution

### Synopsis

R.QT(p,n,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

n: the number of degrees of freedom of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Student t distribution.

R.DT, R.PT.

## R.QTUKEY

R.QTUKEY probability quantile function of the Studentized range distribution

### Synopsis

R.QTUKEY(p,nmeans,df,nranges,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

nmeans: the number of means

df: the number of degrees of freedom of the distribution

nranges: the number of ranges; default is 1

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Studentized range distribution.

## R.QWEIBULL

R.QWEIBULL probability quantile function of the Weibull distribution

### Synopsis

R.QWEIBULL(p,shape,scale,lower_tail,log_p)

### Arguments

p: probability or natural logarithm of the probability

shape: the shape parameter of the distribution

scale: the scale parameter of the distribution

lower_tail: if true (the default), the lower tail of the distribution is considered

log_p: if true, the natural logarithm of the probability is given or returned; defaults to false

### Description

This function returns the probability quantile function, i.e., the inverse of the cumulative distribution function, of the Weibull distribution.

## RANK

RANK rank of a number in a list of numbers

### Synopsis

RANK(x,ref,order)

### Arguments

x: number whose rank you want to find

ref: list of numbers

order: 0 (descending order) or non-zero (ascending order); defaults to 0

### Note

In case of a tie, RANK returns the largest possible rank.

### Microsoft Excel Compatibility

This function is Excel compatible.

## RANK.AVG

RANK.AVG rank of a number in a list of numbers

### Synopsis

RANK.AVG(x,ref,order)

### Arguments

x: number whose rank you want to find

ref: list of numbers

order: 0 (descending order) or non-zero (ascending order); defaults to 0

### Note

In case of a tie, RANK.AVG returns the average rank.

### Microsoft Excel Compatibility

This function is Excel 2010 compatible.

## RAYLEIGH

RAYLEIGH probability density function of the Rayleigh distribution

### Synopsis

RAYLEIGH(x,sigma)

### Arguments

x: number

sigma: scale parameter

## RAYLEIGHTAIL

RAYLEIGHTAIL probability density function of the Rayleigh tail distribution

### Synopsis

RAYLEIGHTAIL(x,a,sigma)

### Arguments

x: number

a: lower limit

sigma: scale parameter

## RSQ

RSQ square of the Pearson correlation coefficient of the paired set of data

### Synopsis

RSQ(array1,array2)

### Arguments

array1: first component values

array2: second component values

### Description

Strings and empty cells are simply ignored.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SFTEST

SFTEST Shapiro-Francia Test of Normality

SFTEST(x)

### Arguments

x: array of sample values

### Description

This function returns an array with the first row giving the p-value of the Shapiro-Francia Test, the second row the test statistic of the test, and the third the number of observations in the sample.

### Note

If there are less than 5 or more than 5000 sample values, SFTEST returns #VALUE!

## SKEW

SKEW unbiased estimate for skewness of a distribution

### Synopsis

SKEW(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

### Note

This is only meaningful if the underlying distribution really has a third moment. The skewness of a symmetric (e.g., normal) distribution is zero. If less than three numbers are given, this function returns a #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SKEWP

SKEWP population skewness of a data set

### Synopsis

SKEWP(number1,number2,…)

### Arguments

number1: first value

number2: second value

### Description

Strings and empty cells are simply ignored.

### Note

If less than two numbers are given, SKEWP returns a #DIV/0! error.

## SLOPE

SLOPE the slope of a linear regression line

### Synopsis

SLOPE(known_ys,known_xs)

### Arguments

known_ys: known y-values

known_xs: known x-values

### Note

If known_xs or known_ys contains no data entries or different number of data entries, this function returns a #N/A error. If the variance of the known_xs is zero, this function returns #DIV/0 error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SMALL

SMALL k-th smallest value in a data set

SMALL(data,k)

### Arguments

data: data set

k: which value to find

### Note

If data set is empty this function returns a #NUM! error. If k <= 0 or k is greater than the number of data items given this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SNORM.DIST.RANGE

SNORM.DIST.RANGE probability of the standard normal distribution over an interval

### Synopsis

SNORM.DIST.RANGE(x1,x2)

### Arguments

x1: start of the interval

x2: end of the interval

### Description

This function returns the cumulative probability over a range of the standard normal distribution; that is the integral over the probability density function from x1 to x2.

### Note

If x1>x2, this function returns a negative value.

## SSMEDIAN

SSMEDIAN median for grouped data

### Synopsis

SSMEDIAN(array,interval)

### Arguments

array: data set

interval: length of each grouping interval, defaults to 1

### Description

The data are assumed to be grouped into intervals of width interval. Each data point in array is the midpoint of the interval containing the true value. The median is calculated by interpolation within the median interval (the interval containing the median value), assuming that the true values within that interval are distributed uniformly:

median = L + interval*(N/2 - CF)/F

where:

L = the lower limit of the median interval

N = the total number of data points

CF = the number of data points below the median interval

F = the number of data points in the median interval

### Note

If array is empty, this function returns a #NUM! error. If interval <= 0, this function returns a #NUM! error. SSMEDIAN does not check whether the data points are at least interval apart.

## STANDARDIZE

STANDARDIZE z-score of a value

### Synopsis

STANDARDIZE(x,mean,stddev)

### Arguments

x: value

mean: mean of the original distribution

stddev: standard deviation of the original distribution

### Note

If stddev is 0 this function returns a #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## STDEV

STDEV sample standard deviation of the given sample

### Synopsis

STDEV(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

STDEV is also known as the N-1-standard deviation.

To obtain the population standard deviation of a whole population use STDEVP.

### Microsoft Excel Compatibility

This function is Excel compatible.

## STDEVA

STDEVA sample standard deviation of the given sample

### Synopsis

STDEVA(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

STDEVA is also known as the N-1-standard deviation.

To obtain the population standard deviation of a whole population use STDEVPA.

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Microsoft Excel Compatibility

This function is Excel compatible.

## STDEVP

STDEVP population standard deviation of the given population

### Synopsis

STDEVP(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

This is also known as the N-standard deviation

### Microsoft Excel Compatibility

This function is Excel compatible.

## STDEVPA

STDEVPA population standard deviation of an entire population

### Synopsis

STDEVPA(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

This is also known as the N-standard deviation

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Microsoft Excel Compatibility

This function is Excel compatible.

## STEYX

STEYX standard error of the predicted y-value in the regression

### Synopsis

STEYX(known_ys,known_xs)

### Arguments

known_ys: known y-values

known_xs: known x-values

### Note

If known_ys and known_xs are empty or have a different number of arguments then this function returns a #N/A error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## SUBTOTAL

SUBTOTAL the subtotal of the given list of arguments

### Synopsis

SUBTOTAL(function_nbr,ref1,ref2,…)

### Arguments

function_nbr: determines which function to use according to the following table:

1 AVERAGE

2 COUNT

3 COUNTA

4 MAX

5 MIN

6 PRODUCT

7 STDEV

8 STDEVP

9 SUM

10 VAR

11 VARP

ref1: first value

ref2: second value

### Microsoft Excel Compatibility

This function is Excel compatible.

COUNT, SUM.

## TDIST

TDIST survival function of the Student t-distribution

### Synopsis

TDIST(x,dof,tails)

### Arguments

x: number

dof: number of degrees of freedom

tails: 1 or 2

### Description

The survival function is 1 minus the cumulative distribution function.

This function is Excel compatible for non-negative x.

### Note

If dof < 1 this function returns a #NUM! error. If tails is neither 1 or 2 this function returns a #NUM! error. The parameterization of this function is different from what is used for, e.g., NORMSDIST. This is a common source of mistakes, but necessary for compatibility.

## TINV

TINV two tailed inverse of the Student t-distribution

TINV(p,dof)

### Arguments

p: probability in both tails

dof: number of degrees of freedom

### Description

This function returns the non-negative value x such that the area under the Student t density with dof degrees of freedom to the right of x is p/2.

### Note

If p < 0 or p > 1 or dof < 1 this function returns a #NUM! error. The parameterization of this function is different from what is used for, e.g., NORMSINV. This is a common source of mistakes, but necessary for compatibility.

### Microsoft Excel Compatibility

This function is Excel compatible.

## TREND

TREND estimates future values of a given data set using a least squares approximation

### Synopsis

TREND(known_ys,known_xs,new_xs,affine)

### Arguments

known_ys: vector of values of dependent variable

known_xs: array of values of independent variables, defaults to a single vector {1,…,n}

new_xs: array of x-values for which to estimate the y-values; defaults to known_xs

affine: if true, the model contains a constant term, defaults to true

### Note

If the length of known_ys does not match the corresponding length of known_xs, this function returns a #NUM! error.

## TRIMMEAN

TRIMMEAN mean of the interior of a data set

### Synopsis

TRIMMEAN(ref,fraction)

### Arguments

ref: list of numbers whose mean you want to calculate

fraction: fraction of the data set excluded from the mean

### Description

If fraction=0.2 and the data set contains 40 numbers, 8 numbers are trimmed from the data set (40 x 0.2): the 4 largest and the 4 smallest. To avoid a bias, the number of points to be excluded is always rounded down to the nearest even number.

### Microsoft Excel Compatibility

This function is Excel compatible.

## TTEST

TTEST p-value for a hypothesis test comparing the means of two populations using the Student t-distribution

### Synopsis

TTEST(array1,array2,tails,type)

### Arguments

array1: sample from the first population

array2: sample from the second population

tails: number of tails to consider

type: Type of test to perform. 1 indicates a test for paired variables, 2 a test of unpaired variables with equal variances, and 3 a test of unpaired variables with unequal variances

### Note

If the data sets contain a different number of data points and the test is paired (type one), TTEST returns the #N/A error. tails and type are truncated to integers. If tails is not one or two, this function returns a #NUM! error. If type is any other than one, two, or three, this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## VAR

VAR sample variance of the given sample

### Synopsis

VAR(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

VAR is also known as the N-1-variance.

### Note

Since the N-1-variance includes Bessel's correction, whereas the N-variance calculated by VARPA or VARP does not, under reasonable conditions the N-1-variance is an unbiased estimator of the variance of the population from which the sample is drawn.

### Microsoft Excel Compatibility

This function is Excel compatible.

## VARA

VARA sample variance of the given sample

### Synopsis

VARA(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

VARA is also known as the N-1-variance.

To get the true variance of a complete population use VARPA.

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Note

Since the N-1-variance includes Bessel's correction, whereas the N-variance calculated by VARPA or VARP does not, under reasonable conditions the N-1-variance is an unbiased estimator of the variance of the population from which the sample is drawn.

### Microsoft Excel Compatibility

This function is Excel compatible.

VAR, VARPA.

## VARP

VARP variance of an entire population

### Synopsis

VARP(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

VARP is also known as the N-variance.

## VARPA

VARPA variance of an entire population

### Synopsis

VARPA(area1,area2,…)

### Arguments

area1: first cell area

area2: second cell area

### Description

VARPA is also known as the N-variance.

Numbers, text and logical values are included in the calculation too. If the cell contains text or the argument evaluates to FALSE, it is counted as value zero (0). If the argument evaluates to TRUE, it is counted as one (1). Note that empty cells are not counted.

### Microsoft Excel Compatibility

This function is Excel compatible.

VARA, VARP.

## WEIBULL

WEIBULL probability density or cumulative distribution function of the Weibull distribution

### Synopsis

WEIBULL(x,alpha,beta,cumulative)

### Arguments

x: number

alpha: scale parameter

beta: scale parameter

cumulative: whether to evaluate the density function or the cumulative distribution function

### Description

If the cumulative boolean is true it will return: 1 - exp (-(x/beta)^alpha), otherwise it will return (alpha/beta^alpha) * x^(alpha-1) * exp(-(x/beta^alpha)).

### Note

If x < 0 this function returns a #NUM! error. If alpha <= 0 or beta <= 0 this function returns a #NUM! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

## ZTEST

ZTEST the probability of observing a sample mean as large as or larger than the mean of the given sample

### Synopsis

ZTEST(ref,x,stddev)

### Arguments

ref: data set (sample)

x: population mean

stddev: population standard deviation, defaults to the sample standard deviation

### Description

ZTEST calculates the probability of observing a sample mean as large as or larger than the mean of the given sample for samples drawn from a normal distribution with mean x and standard deviation stddev.

### Note

If ref contains less than two data items ZTEST returns #DIV/0! error.

### Microsoft Excel Compatibility

This function is Excel compatible.

### OpenDocument Format (ODF) Compatibility

This function is OpenFormula compatible.