# Statistical Functions Part Five

## VARP

Calculates a variance based on the entire population.

VARP(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

=VARP(A1:A50)

## VAR.P

Calculates a variance based on the entire population.

VAR.P(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

=VAR.P(A1:A50)

## T.INV.2T

Calculates the inverse of the two-tailed Student's t-distribution , which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

T.INV.2T(Number; DegreesFreedom)

Number is the probability associated with the two-tailed t-distribution.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

=T.INV.2T(0.25; 10) returns 1.221255395.

## T.DIST.RT

Calculates the right-tailed Student's t-distribution, which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

T.DIST.RT(Number; DegreesFreedom)

Number is the value for which the t-distribution is calculated.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

=T.DIST.RT(1; 10) returns 0.1704465662.

## STDEV.S

Calculates the standard deviation based on sample of the population.

STDEV.S(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least two values.

=STDEV.S(A1:A50) returns a standard deviation of the data referenced.

## STDEVP

Calculates the standard deviation based on the entire population.

STDEVP(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

=STDEVP(A1:A50) returns a standard deviation of the data referenced.

## STDEV.P

Calculates the standard deviation based on the entire population.

STDEV.P(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

=STDEV.P(A1:A50) returns a standard deviation of the data referenced.

## STDEVPA

Calculates the standard deviation based on the entire population.

STDEVPA(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

Text has the value 0.

=STDEVPA(A1:A50) returns the standard deviation of the data referenced.

## STDEVA

Calculates the standard deviation of an estimation based on a sample.

STDEVA(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least two values. Text has the value 0.

=STDEVA(A1:A50) returns the estimated standard deviation based on the data referenced.

## T.DIST.2T

Calculates the two-tailed Student's t distribution, which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

T.DIST.2T(Number; DegreesFreedom)

Number is the value for which the t-distribution is calculated.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

=T.DIST.2T(1; 10) returns 0.3408931323.

## VARPA

Calculates the variance based on the entire population. The value of text is 0.

VARPA(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

=VARPA(A1:A50)

## STANDARDISE

Converts a random variable to a normalised value.

STANDARDISE(Number; Mean; StandardDeviation)

Number is the value to be standardised.

Mean is the arithmetic mean of the distribution.

StandardDeviation is the standard deviation of the distribution.

=STANDARDISE(11;10;1) returns 1. The value 11 in a normal distribution with a mean of 10 and a standard deviation of 1 is as much above the mean of 10, as the value 1 is above the mean of the standard normal distribution.

## VARA

Estimates a variance based on a sample. The value of text is 0.

VARA(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least two values.

=VARA(A1:A50)

## STDEV

Estimates the standard deviation based on a sample.

STDEV(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least two values.

=STDEV(A1:A50) returns the estimated standard deviation based on the data referenced.

## VAR

Estimates the variance based on a sample.

VAR(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least two values.

=VAR(A1:A50)

## VAR.S

Estimates the variance based on a sample.

VAR.S(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least two values.

=VAR.S(A1:A50)

## FORECAST

Extrapolates future values based on existing x- and y-values.

FORECAST(Value; DataY; DataX)

Value is the x-value for which the y-value on the linear regression is to be returned.

DataY is the array or range of known y's.

DataX is the array or range of known x's.

=FORECAST(50;A1:A50;B1:B50) returns the y-value expected for the x-value of 50 if the x- and y-values in both references are linked by a linear trend.

## FORECAST.LINEAR

Extrapolates future values based on existing x- and y-values.

FORECAST.LINEAR(Value; DataY; DataX)

Value is the x-value for which the y-value on the linear regression is to be returned.

DataY is the array or range of known y-values.

DataX is the array or range of known x-values.

=FORECAST(50;A1:A50;B1:B50) returns the y-value expected for the x-value of 50 if the x- and y-values in both references are linked by a linear trend.

## NORMSINV

Returns the inverse of the standard normal cumulative distribution.

NORMSINV(Number)

Number is the probability to which the inverse standard normal distribution is calculated.

=NORMSINV(0.908789) returns 1.3333.

## NORM.S.INV

Returns the inverse of the standard normal cumulative distribution.

NORM.S.INV(Number)

Number is the probability to which the inverse standard normal distribution is calculated.

=NORM.S.INV(0.908789) returns 1.333334673.

## TINV

Returns the inverse of the t-distribution.

TINV(Number; DegreesFreedom)

Number is the probability associated with the two-tailed t-distribution.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

=TINV(0.1;6) returns 1.94

## PERMUTATIONA

Returns the number of permutations for a given number of objects (repetition allowed).

PERMUTATIONA(Count1; Count2)

Count1 is the total number of objects.

Count2 is the number of objects in each permutation.

How often can 2 objects be selected from a set of 11 objects?

=PERMUTATIONA(11;2) returns 121.

=PERMUTATIONA(6;3) returns 216. There are 216 different possibilities to put a sequence of 3 playing cards together out of six playing cards if every card is returned before the next one is drawn.

## PERMUT

Returns the number of permutations for a given number of objects.

PERMUT(Count1; Count2)

Count1 is the total number of objects.

Count2 is the number of objects in each permutation.

=PERMUT(6;3) returns 120. There are 120 different possibilities, to pick a sequence of 3 playing cards out of 6 playing cards.

## T.INV

Returns the one tailed inverse of the t-distribution.

T.INV(Number; DegreesFreedom)

Number is the probability associated with the one-tailed t-distribution.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

=T.INV(0.1;6) returns -1.4397557473.

## TTEST

Returns the probability associated with a Student's t-Test.

TTEST(Data1; Data2; Mode; Type)

Data1 is the dependent array or range of data for the first record.

Data2 is the dependent array or range of data for the second record.

Mode = 1 calculates the one-tailed test, Mode = 2 the two- tailed test.

Type is the kind of t-test to perform. Type 1 means paired. Type 2 means two samples, equal variance (homoscedastic). Type 3 means two samples, unequal variance (heteroscedastic).

=TTEST(A1:A50;B1:B50;2;2)

## T.TEST

Returns the probability associated with a Student's t-Test.

T.TEST(Data1; Data2; Mode; Type)

Data1 is the dependent array or range of data for the first record.

Data2 is the dependent array or range of data for the second record.

Mode = 1 calculates the one-tailed test, Mode = 2 the two-tailed test.

Type is the kind of t-test to perform. Type 1 means paired. Type 2 means two samples, equal variance (homoscedastic). Type 3 means two samples, unequal variance (heteroscedastic).

=T.TEST(A1:A50;B1:B50;2;2)

## PROB

Returns the probability that values in a range are between two limits. If there is no End value, this function calculates the probability based on the principle that the Data values are equal to the value of Start.

PROB(Data; Probability; Start [; End])

Data is the array or range of data in the sample.

Probability is the array or range of the corresponding probabilities.

Start is the start value of the interval over which the probabilities are to be summed.

End (optional) is the end value of the interval whose probabilities are to be summed. If this parameter is missing, the probability for the Start value is calculated.

=PROB(A1:A50;B1:B50;50;60) returns the probability with which a value within the range of A1:A50 is also within the given limits of 50 to 60. Every value in the range of A1:A50 has a probability within the range of B1:B50.

## RANK

Returns the rank of a number in a sample.

RANK(Value; Data [; Type])

Value is the value, whose rank is to be determined.

Data is the array or range of data in the sample.

Type (optional) is the sequence order.

Type = 0 means descending from the last item of the array to the first (this is the default),

Type = 1 means ascending from the first item of the range to the last.

=RANK(A10;A1:A50) returns the ranking of the value in A10 in value range A1:A50. If Value does not exist within the range an error message is displayed.

## SKEW

Returns the skewness of a distribution.

SKEW(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

The parameters should specify at least three values.

=SKEW(A1:A50) calculates the value of skew for the data referenced.

## SLOPE

Returns the slope of the linear regression line. The slope is adapted to the data points set in the y- and x-values.

SLOPE(DataY; DataX)

DataY is the array or matrix of y-data.

DataX is the array or matrix of x-data.

=SLOPE(A1:A50;B1:B50)

## STEYX

Returns the standard error of the predicted y-value for each x-value in the regression.

STEYX(DataY; DataX)

DataY is the array or matrix of y-data.

DataX is the array or matrix of x-data.

=STEYX(A1:A50;B1:B50)

## NORMSDIST

Returns the standard normal cumulative distribution function. The distribution has a mean of zero and a standard deviation of one.

It is GAUSS(x)=NORMSDIST(x)-0.5

NORMSDIST(Number)

Number is the value to which the standard normal cumulative distribution is calculated.

=NORMSDIST(1) returns 0.84. The area below the standard normal distribution curve to the left of x-value 1 is 84% of the total area.

## NORM.S.DIST

Returns the standard normal cumulative distribution function. The distribution has a mean of zero and a standard deviation of one.

NORM.S.DIST(Number; Cumulative)

Number is the value to which the standard normal cumulative distribution is calculated.

Cumulative 0 or FALSE calculates the probability density function. Any other value or TRUE calculates the cumulative distribution function.

=NORM.S.DIST(1;0) returns 0.2419707245.

=NORM.S.DIST(1;1) returns 0.8413447461. The area below the standard normal distribution curve to the left of X value 1 is 84% of the total area.

## RANK.AVG

Returns the statistical rank of a given value, within a supplied array of values. If there are duplicate values in the list, the average rank is returned.

The difference between RANK.AVG and RANK.EQ occurs when there are duplicates in the list of values. The RANK.EQ function returns the lower rank, whereas the RANK.AVG function returns the average rank.

RANK.AVG(Value; Data [; Type])

Value is the value, whose rank is to be determined.

Data is the array or range of data in the sample.

Type (optional) is the sequence order.

Type = 0 means descending from the last item of the array to the first (this is the default),

Type = 1 means ascending from the first item of the range to the last.

=RANK.AVG(A10;A1:A50) returns the ranking of the value in A10 in value range A1:A50. If Value does not exist within the range an error message is displayed.

## RANK.EQ

Returns the statistical rank of a given value, within a supplied array of values. If there are duplicate values in the list, these are given the same rank.

The difference between RANK.AVG and RANK.EQ occurs when there are duplicates in the list of values. The RANK.EQ function returns the lower rank, whereas the RANK.AVG function returns the average rank.

RANK.EQ(Value; Data [; Type])

Value is the value, whose rank is to be determined.

Data is the array or range of data in the sample.

Type (optional) is the sequence order.

Type = 0 means descending from the last item of the array to the first (this is the default),

Type = 1 means ascending from the first item of the range to the last.

=RANK.EQ(A10;A1:A50) returns the ranking of the value in A10 in value range A1:A50. If Value does not exist within the range an error message is displayed.

## DEVSQ

Returns the sum of squares of deviations based on a sample mean.

DEVSQ(Number 1 [; Number 2 [; â€¦ [; Number 255]]])

=DEVSQ(A1:A50)

## TDIST

Returns the t-distribution.

TDIST(Number; DegreesFreedom; Mode)

Number is the value for which the t-distribution is calculated.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

Mode = 1 returns the one-tailed test, Mode = 2 returns the two-tailed test.

=TDIST(12;5;1)

## T.DIST

Returns the t-distribution.

T.DIST(Number; DegreesFreedom; Cumulative)

Number is the value for which the t-distribution is calculated.

DegreesFreedom is the number of degrees of freedom for the t-distribution.

Cumulative = 0 or FALSE returns the probability density function, 1 or TRUE returns the cumulative distribution function.

=T.DIST(1; 10; TRUE) returns 0.8295534338

## WEIBULL

Returns the values of the Weibull distribution.

The Weibull distribution is a continuous probability distribution, with parameters Alpha > 0 (shape) and Beta > 0 (scale).

If C is 0, WEIBULL calculates the probability density function.

If C is 1, WEIBULL calculates the cumulative distribution function.

WEIBULL(Number; Alpha; Beta; C)

Number is the value at which to calculate the Weibull distribution.

Alpha is the shape parameter of the Weibull distribution.

Beta is the scale parameter of the Weibull distribution.

C indicates the type of function. If C=0 the probability density function is calculated, if C=1 the cumulative distribution is calculated.

=WEIBULL(2;1;1;1) returns 0.86.

See also the Wiki page.

## WEIBULL.DIST

Returns the values of the Weibull distribution.

The Weibull distribution is a continuous probability distribution, with parameters Alpha > 0 (shape) and Beta > 0 (scale).

If C is 0, WEIBULL.DIST calculates the probability density function.

If C is 1, WEIBULL.DIST calculates the cumulative distribution function.

WEIBULL.DIST(Number; Alpha; Beta; C)

Number is the value at which to calculate the Weibull distribution.

Alpha is the shape parameter of the Weibull distribution.

Beta is the scale parameter of the Weibull distribution.

C indicates the type of function. If C=0 the probability density function is calculated, if C=1 the cumulative distribution is calculated.

=WEIBULL.DIST(2;1;1;1) returns 0.8646647168.

See also the Wiki page.