# Statistical Functions Part Two

## Contents

## ZTEST

Calculates the probability of observing a z-statistic greater than the one computed based on a sample.

### Syntax

`ZTEST(Data; mu; Sigma)`

**Data** is the given sample, drawn from a normally distributed population.

**mu** is the known mean of the population.

**Sigma** (optional) is the known standard deviation of the population. If omitted, the standard deviation of the given sample is used.

See also the Wiki page.

## Z.TEST

Calculates the probability of observing a z-statistic greater than the one computed based on a sample.

### Syntax

`Z.TEST(Data; mu; Sigma)`

**Data** is the given sample, drawn from a normally distributed population.

**mu** is the known mean of the population.

**Sigma** (optional) is the known standard deviation of the population. If omitted, the standard deviation of the given sample is used.

### Example

`=Z.TEST(A2:A20; 9; 2)`

returns the result of a z-test on a sample A2:A20 drawn from a population with known mean 9 and known standard deviation 2.

## TRIMMEAN

Returns the mean of a data set without the Alpha percent of data at the margins.

### Syntax

`TRIMMEAN(Data; Alpha)`

**Data** is the array of data in the sample.

**Alpha** is the percentage of the marginal data that will not be taken into consideration.

### Example

`=TRIMMEAN(A1:A50; 0.1)`

calculates the mean value of numbers in A1:A50, without taking into consideration the 5 percent of the values representing the highest values and the 5 percent of the values representing the lowest ones. The percentage numbers refer to the amount of the untrimmed mean value, not to the number of summands.

## HYPGEOM.DIST

Returns the hypergeometric distribution.

### Syntax

`HYPGEOM.DIST(X; NSample; Successes; NPopulation; Cumulative)`

**X** is the number of results achieved in the random sample.

**NSample** is the size of the random sample.

**Successes** is the number of possible results in the total population.

**NPopulation** is the size of the total population.

**Cumulative** : 0 or False calculates the probability density function. Other values or True calculates the cumulative distribution function.

### Examples

`=HYPGEOM.DIST(2;2;90;100;0)`

yields 0.8090909091. If 90 out of 100 pieces of buttered toast fall from the table and hit the floor with the buttered side first, then if 2 pieces of buttered toast are dropped from the table, the probability is 81%, that both will strike buttered side first.

`=HYPGEOM.DIST(2;2;90;100;1)`

yields 1.

## HYPGEOMDIST

Returns the hypergeometric distribution.

### Syntax

`HYPGEOMDIST(X; NSample; Successes; NPopulation)`

**X** is the number of results achieved in the random sample.

**NSample** is the size of the random sample.

**Successes** is the number of possible results in the total population.

**NPopulation** is the size of the total population.

### Example

`=HYPGEOMDIST(2;2;90;100)`

yields 0.81. If 90 out of 100 pieces of buttered toast fall from the table and hit the floor with the buttered side first, then if 2 pieces of buttered toast are dropped from the table, the probability is 81%, that both will strike buttered side first.

## HARMEAN

Returns the harmonic mean of a data set.

### Syntax

`HARMEAN(Number1; Number2; ...Number30)`

**Number1,Number2,...Number30** are up to 30 values or ranges, that can be used to calculate the harmonic mean.

### Example

`=HARMEAN(23;46;69)`

= 37.64. The harmonic mean of this random sample is thus 37.64

## GEOMEAN

Returns the geometric mean of a sample.

### Syntax

`GEOMEAN(Number1; Number2; ...Number30)`

**Number1, Number2,...Number30** are numeric arguments or ranges that represent a random sample.

### Example

`=GEOMEAN(23;46;69)`

= 41.79. The geometric mean value of this random sample is therefore 41.79.

## GAUSS

Returns the standard normal cumulative distribution.

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

### Syntax

`GAUSS(Number)`

**Number** is the value for which the value of the standard normal distribution is to be calculated.

### Example

`=GAUSS(0.19)`

= 0.08

`=GAUSS(0.0375)`

= 0.01

## GAMMALN.PRECISE

Returns the natural logarithm of the Gamma function: G(x).

### Syntax

`GAMMALN.PRECISE(Number)`

**Number** is the value for which the natural logarithm of the Gamma function is to be calculated.

### Example

`=GAMMALN.PRECISE(2)`

yields 0.

## GAMMALN

Returns the natural logarithm of the Gamma function: G(x).

### Syntax

`GAMMALN(Number)`

**Number** is the value for which the natural logarithm of the Gamma function is to be calculated.

### Example

`=GAMMALN(2)`

yields 0.

## GAMMAINV

Returns the inverse of the Gamma cumulative distribution GAMMADIST. This function allows you to search for variables with different distribution.

### Syntax

`GAMMAINV(Number; Alpha; Beta)`

**Number** is the probability value for which the inverse Gamma distribution is to be calculated.

**Alpha** is the parameter Alpha of the Gamma distribution.

**Beta** is the parameter Beta of the Gamma distribution.

### Example

`=GAMMAINV(0.8;1;1)`

yields 1.61.

## GAMMA.INV

Returns the inverse of the Gamma cumulative distribution GAMMADIST. This function allows you to search for variables with different distribution.

This function is identical to GAMMAINV and was introduced for interoperability with other office suites.

### Syntax

`GAMMA.INV(Number; Alpha; Beta)`

**Number** is the probability value for which the inverse Gamma distribution is to be calculated.

**Alpha** is the parameter Alpha of the Gamma distribution.

**Beta** is the parameter Beta of the Gamma distribution.

### Example

`=GAMMA.INV(0.8;1;1)`

yields 1.61.

## GAMMA.DIST

Returns the values of a Gamma distribution.

The inverse function is GAMMAINV or GAMMA.INV.

This function is identical to GAMMADIST and was introduced for interoperability with other office suites.

### Syntax

`GAMMA.DIST(Number; Alpha; Beta; C)`

**Number** is the value for which the Gamma distribution is to be calculated.

**Alpha** is the parameter Alpha of the Gamma distribution.

**Beta** is the parameter Beta of the Gamma distribution

**C** (optional) = 0 or False calculates the density function **C** = 1 or True calculates the distribution.

### Example

`=GAMMA.DIST(2;1;1;1)`

yields 0.86.

## GAMMADIST

Returns the values of a Gamma distribution.

The inverse function is GAMMAINV.

### Syntax

`GAMMADIST(Number; Alpha; Beta; C)`

**Number** is the value for which the Gamma distribution is to be calculated.

**Alpha** is the parameter Alpha of the Gamma distribution.

**Beta** is the parameter Beta of the Gamma distribution

**C** (optional) = 0 or False calculates the density function **C** = 1 or True calculates the distribution.

### Example

`=GAMMADIST(2;1;1;1)`

yields 0.86.

## GAMMA

Returns the Gamma function value. Note that GAMMAINV is not the inverse of GAMMA, but of GAMMADIST.

### Syntax

**Number** is the number for which the Gamma function value is to be calculated.

## FTEST

Returns the result of an F test.

### Syntax

`FTEST(Data1; Data2)`

**Data1** is the first record array.

**Data2** is the second record array.

### Example

`=FTEST(A1:A30;B1:B12)`

calculates whether the two data sets are different in their variance and returns the probability that both sets could have come from the same total population.

## FISHERINV

Returns the inverse of the Fisher transformation for x and creates a function close to a normal distribution.

### Syntax

`FISHERINV(Number)`

**Number** is the value that is to undergo reverse-transformation.

### Example

`=FISHERINV(0.5)`

yields 0.46.

## FISHER

Returns the Fisher transformation for x and creates a function close to a normal distribution.

### Syntax

`FISHER(Number)`

**Number** is the value to be transformed.

### Example

`=FISHER(0.5)`

yields 0.55.

## FINV

Returns the inverse of the F probability distribution. The F distribution is used for F tests in order to set the relation between two differing data sets.

### Syntax

`FINV(Number; DegreesFreedom1; DegreesFreedom2)`

**Number** is probability value for which the inverse F distribution is to be calculated.

**DegreesFreedom1** is the number of degrees of freedom in the numerator of the F distribution.

**DegreesFreedom2** is the number of degrees of freedom in the denominator of the F distribution.

### Example

`=FINV(0.5;5;10)`

yields 0.93.

## F.TEST

Returns the result of an F test.

### Syntax

`F.TEST(Data1; Data2)`

**Data1** is the first record array.

**Data2** is the second record array.

### Example

`=F.TEST(A1:A30;B1:B12)`

calculates whether the two data sets are different in their variance and returns the probability that both sets could have come from the same total population.

## F.INV.RT

Returns the inverse right tail of the F distribution.

### Syntax

`F.INV.RT(Number; DegreesFreedom1; DegreesFreedom2)`

**Number** is probability value for which the inverse F distribution is to be calculated.

**DegreesFreedom1** is the number of degrees of freedom in the numerator of the F distribution.

**DegreesFreedom2** is the number of degrees of freedom in the denominator of the F distribution.

### Example

`=F.INV.RT(0.5;5;10)`

yields 0.9319331609.

## F.INV

Returns the inverse of the cumulative F distribution. The F distribution is used for F tests in order to set the relation between two differing data sets.

### Syntax

`F.INV(Number; DegreesFreedom1; DegreesFreedom2)`

**Number** is probability value for which the inverse F distribution is to be calculated.

**DegreesFreedom1** is the number of degrees of freedom in the numerator of the F distribution.

**DegreesFreedom2** is the number of degrees of freedom in the denominator of the F distribution.

### Example

`=F.INV(0.5;5;10)`

yields 0.9319331609.

## F.DIST.RT

Calculates the values of the right tail of the F distribution.

### Syntax

`F.DIST.RT(Number; DegreesFreedom1; DegreesFreedom2)`

**Number** is the value for which the F distribution is to be calculated.

**degreesFreedom1** is the degrees of freedom in the numerator in the F distribution.

**degreesFreedom2** is the degrees of freedom in the denominator in the F distribution.

### Example

`=F.DIST.RT(0.8;8;12)`

yields 0.6143396437.

## F.DIST

Calculates the values of the left tail of the F distribution.

### Syntax

`F.DIST(Number; DegreesFreedom1; DegreesFreedom2; Cumulative)`

**Number** is the value for which the F distribution is to be calculated.

**degreesFreedom1** is the degrees of freedom in the numerator in the F distribution.

**degreesFreedom2** is the degrees of freedom in the denominator in the F distribution.

**Cumulative** = 0 or False calculates the density function **Cumulative** = 1 or True calculates the distribution.

### Example

`=F.DIST(0.8;8;12;0)`

yields 0.7095282499.

`=F.DIST(0.8;8;12;1)`

yields 0.3856603563.

## FDIST

Calculates the values of an F distribution.

### Syntax

`FDIST(Number; DegreesFreedom1; DegreesFreedom2)`

**Number** is the value for which the F distribution is to be calculated.

**degreesFreedom1** is the degrees of freedom in the numerator in the F distribution.

**degreesFreedom2** is the degrees of freedom in the denominator in the F distribution.

### Example

`=FDIST(0.8;8;12)`

yields 0.61.