# Statistical Functions Part Four

## QUARTILE.INC

Returns the quartile of a data set. The difference between `QUARTILE.INC` and `QUARTILE.EXC` is that the `QUARTILE.INC` function bases its calculation on a percentile range of 0 to 1 inclusive, whereas the `QUARTILE.EXC` function bases its calculation on a percentile range of 0 to 1 exclusive.

### Syntax

`QUARTILE.INC(Data; Type)`

Data represents the array of data in the sample.

Type represents the type of quartile. (0 = MIN, 1 = 25%, 2 = 50% (MEDIAN), 3 = 75% and 4 = MAX.)

### Example

`=QUARTILE.INC(A1:A50;2)` returns the value of which 50% of the scale corresponds to the lowest to highest values in the range A1:A50.

## QUARTILE.EXC

Returns a requested quartile of a supplied range of values, based on a percentile range of 0 to 1 exclusive. The difference between `QUARTILE.INC` and `QUARTILE.EXC` is that the `QUARTILE.INC` function bases its calculation on a percentile range of 0 to 1 inclusive, whereas the `QUARTILE.EXC` function bases its calculation on a percentile range of 0 to 1 exclusive.

### Syntax

`QUARTILE.EXC(Data; Type)`

Data represents the range of data values for which you want to calculate the specified quartile.

Type An integer between 1 and 3, representing the required quartile. (if type = 1 or 3, the supplied array must contain more than 2 values)

### Example

`=QUARTILE.EXC(A1:A50;2)` returns the value of which 50% of the scale corresponds to the lowest to highest values in the range A1:A50.

## QUARTILE

Returns the quartile of a data set.

### Syntax

`QUARTILE(Data; Type)`

Data represents the array of data in the sample.

Type represents the type of quartile. (0 = MIN, 1 = 25%, 2 = 50% (MEDIAN), 3 = 75% and 4 = MAX.)

### Example

`=QUARTILE(A1:A50;2)` returns the value of which 50% of the scale corresponds to the lowest to highest values in the range A1:A50.

## POISSON.DIST

Returns the Poisson distribution.

### Syntax

`POISSON.DIST(Number; Mean; C)`

Number represents the value based on which the Poisson distribution is calculated.

Mean represents the middle value of the Poisson distribution.

C (optional) = 0 or False calculates the density function; C = 1 or True calculates the distribution. When omitted, the default value True is inserted when you save the document, for best compatibility with other programs and older versions of LibreOffice.

### Example

`=POISSON.DIST(60;50;1)` returns 0.9278398202.

## POISSON

Returns the Poisson distribution.

### Syntax

`POISSON(Number; Mean; C)`

Number represents the value based on which the Poisson distribution is calculated.

Mean represents the middle value of the Poisson distribution.

C (optional) = 0 or False calculates the density function; C = 1 or True calculates the distribution. When omitted, the default value True is inserted when you save the document, for best compatibility with other programs and older versions of LibreOffice.

### Example

`=POISSON(60;50;1)` returns 0.93.

## PHI

Returns the values of the distribution function for a standard normal distribution.

### Syntax

`PHI(Number)`

Number represents the value based on which the standard normal distribution is calculated.

### Example

`=PHI(2.25)` = 0.03

`=PHI(-2.25)` = 0.03

`=PHI(0)` = 0.4

## PERCENTRANK.INC

Returns the relative position, between 0 and 1 (inclusive), of a specified value within a supplied array. The difference between `PERCENTRANK.INC` and `PERCENTRANK.EXC` is that `PERCENTRANK.INC` calculates a value in the range 0 to 1 inclusive, whereas the `PERCENTRANK.EXC` function calculates a value in the range 0 to 1 exclusive.

### Syntax

`PERCENTRANK.INC(Data; Value; Significance)`

Data represents the array of data in the sample.

Value represents the value whose percentile rank must be determined.

Significance An optional argument that specifies the number of significant digits that the returned percentage value is rounded to.

### Example

`=PERCENTRANK.INC(A1:A50;50)` returns the percentage rank of the value 50 from the total range of all values found in A1:A50. If 50 falls outside the total range, an error message will appear.

## PERCENTRANK.EXC

Returns the relative position, between 0 and 1 (exclusive), of a specified value within a supplied array. The difference between `PERCENTRANK.INC` and `PERCENTRANK.EXC` is that `PERCENTRANK.INC` calculates a value in the range 0 to 1 inclusive, whereas the `PERCENTRANK.EXC` function calculates a value in the range 0 to 1 exclusive.

### Syntax

`PERCENTRANK.EXC(Data; Value; Significance)`

Data represents the array of data in the sample.

Value represents the value whose percentile rank must be determined.

Significance An optional argument that specifies the number of significant digits that the returned percentage value is rounded to.

### Example

`=PERCENTRANK.EXC(A1:A50;50)` returns the percentage rank of the value 50 from the total range of all values found in A1:A50. If 50 falls outside the total range, an error message will appear.

## PERCENTRANK

Returns the percentage rank of a value in a sample.

### Syntax

`PERCENTRANK(Data; Value)`

Data represents the array of data in the sample.

Value represents the value whose percentile rank must be determined.

### Example

`=PERCENTRANK(A1:A50;50)` returns the percentage rank of the value 50 from the total range of all values found in A1:A50. If 50 falls outside the total range, an error message will appear.

## PERCENTILE.INC

Returns the alpha-percentile of data values in an array. A percentile returns the scale value for a data series which goes from the smallest (Alpha=0) to the largest value (alpha=1) of a data series. For `Alpha` = 25%, the percentile means the first quartile; `Alpha` = 50% is the MEDIAN. The difference between `PERCENTILE.INC` and `PERCENTILE.EXC` is that, in the `PERCENTILE.INC` function the value of alpha is is within the range 0 to 1 inclusive, and in the `PERCENTILE.EXC` function, the value of alpha is within the range 0 to 1 exclusive.

### Syntax

`PERCENTILE.INC(Data; Alpha)`

Data represents the array of data.

Alpha represents the percentage of the scale between 0 and 1.

### Example

`=PERCENTILE.INC(A1:A50;0.1)` represents the value in the data set, which equals 10% of the total data scale in A1:A50.

## PERCENTILE.EXC

Returns the `Alpha`'th percentile of a supplied range of values for a given value of `Alpha`, within the range 0 to 1 (exclusive). A percentile returns the scale value for a data series which goes from the smallest (`Alpha=0`) to the largest value (`Alpha=1`) of a data series. For `Alpha` = 25%, the percentile means the first quartile; `Alpha` = 50% is the MEDIAN. If `Alpha` is not a multiple of `1/(n+1)`, (where n is the number of values in the supplied array), the function interpolates between the values in the supplied array, to calculate the percentile value. However, if `Alpha` is less than `1/(n+1)` or `Alpha` is greater than `n/(n+1)`, the function is unable to interpolate, and so returns an error. The difference between `PERCENTILE.INC` and `PERCENTILE.EXC` is that, in the `PERCENTILE.INC` function the value of alpha is is within the range 0 to 1 inclusive, and in the `PERCENTILE.EXC` function, the value of alpha is within the range 0 to 1 exclusive.

### Syntax

`PERCENTILE.EXC(Data; Alpha)`

Data represents the array of data.

Alpha represents the percentage of the scale between 0 and 1.

### Example

`=PERCENTILE.EXC(A1:A50;10%)` represents the value in the data set, which equals 10% of the total data scale in A1:A50.

## PERCENTILE

Returns the alpha-percentile of data values in an array. A percentile returns the scale value for a data series which goes from the smallest (Alpha=0) to the largest value (alpha=1) of a data series. For `Alpha` = 25%, the percentile means the first quartile; `Alpha` = 50% is the MEDIAN.

### Syntax

`PERCENTILE(Data; Alpha)`

Data represents the array of data.

Alpha represents the percentage of the scale between 0 and 1.

### Example

`=PERCENTILE(A1:A50;0.1)` represents the value in the data set, which equals 10% of the total data scale in A1:A50.

## PEARSON

Returns the Pearson product moment correlation coefficient r.

### Syntax

`PEARSON(Data1; Data2)`

Data1 represents the array of the first data set.

Data2 represents the array of the second data set.

### Example

`=PEARSON(A1:A30;B1:B30)` returns the Pearson correlation coefficient of both data sets.

## NORMINV

Returns the inverse of the normal cumulative distribution.

### Syntax

`NORMINV(Number; Mean; StDev)`

Number represents the probability value used to determine the inverse normal distribution.

Mean represents the mean value in the normal distribution.

StDev represents the standard deviation of the normal distribution.

### Example

`=NORMINV(0.9;63;5)` returns 69.41. If the average egg weighs 63 grams with a standard deviation of 5, then there will be 90% probability that the egg will not be heavier than 69.41g grams.

## NORM.INV

Returns the inverse of the normal cumulative distribution.

### Syntax

`NORM.INV(Number; Mean; StDev)`

Number represents the probability value used to determine the inverse normal distribution.

Mean represents the mean value in the normal distribution.

StDev represents the standard deviation of the normal distribution.

### Example

`=NORM.INV(0.9;63;5)` returns 69.4077578277. If the average egg weighs 63 grams with a standard deviation of 5, then there will be 90% probability that the egg will not be heavier than 69.41g grams.

## NORM.DIST

Returns the density function or the normal cumulative distribution.

### Syntax

`NORM.DIST(Number; Mean; StDev; C)`

Number is the value of the distribution based on which the normal distribution is to be calculated.

Mean is the mean value of the distribution.

StDev is the standard deviation of the distribution.

C = 0 calculates the density function, C = 1 calculates the distribution.

### Example

`=NORM.DIST(70;63;5;0)` returns 0.029945493.

`=NORM.DIST(70;63;5;1)` returns 0.9192433408.

## NORMDIST

Returns the density function or the normal cumulative distribution.

### Syntax

`NORMDIST(Number; Mean; StDev; C)`

Number is the value of the distribution based on which the normal distribution is to be calculated.

Mean is the mean value of the distribution.

StDev is the standard deviation of the distribution.

C is optional. C = 0 calculates the density function, C = 1 calculates the distribution.

### Example

`=NORMDIST(70;63;5;0)` returns 0.03.

`=NORMDIST(70;63;5;1)` returns 0.92.

## NEGBINOM.DIST

Returns the negative binomial density or distribution function.

### Syntax

`NEGBINOM.DIST(X; R; SP; Cumulative)`

X represents the value returned for unsuccessful tests.

R represents the value returned for successful tests.

SP is the probability of the success of an attempt.

Cumulative = 0 calculates the density function, Cumulative = 1 calculates the distribution.

### Example

`=NEGBINOM.DIST(1;1;0.5;0)` returns 0.25.

`=NEGBINOM.DIST(1;1;0.5;1)` returns 0.75.

## NEGBINOMDIST

Returns the negative binomial distribution.

### Syntax

`NEGBINOMDIST(X; R; SP)`

X represents the value returned for unsuccessful tests.

R represents the value returned for successful tests.

SP is the probability of the success of an attempt.

### Example

`=NEGBINOMDIST(1;1;0.5)` returns 0.25.

## MODE.SNGL

Returns the most frequently occurring, or repetitive, value in an array or range of data. If there are several values with the same frequency, it returns the smallest value. An error occurs when a value doesn't appear twice.

### Syntax

`MODE.SNGL(Number1; Number2; ...Number30)`

Number1; Number2;...Number30 are numerical values or ranges. If the data set contains no duplicate data points, MODE.SNGL returns the #VALUE! error value.

### Example

`=MODE.SNGL(A1:A50)`

## MODE.MULT

Returns a vertical array of the statistical modes (the most frequently occurring values) within a list of supplied numbers.

### Syntax

`MODE.MULT(Number1; Number2; ...Number30)`

Number1; Number2;...Number30 are numerical values or ranges. As the MODE.MULT function returns an array of values, it must be entered as an array formula. If the function is not entered as an array formula, only the first mode is returned, which is the same as using the MODE.SNGL function.

### Example

`=MODE.MULT(A1:A50)`

## MODE

Returns the most common value in a data set. If there are several values with the same frequency, it returns the smallest value. An error occurs when a value doesn't appear twice.

### Syntax

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

Number1; Number2;...Number30 are numerical values or ranges.

### Example

`=MODE(A1:A50)`

## MINA

Returns the minimum value in a list of arguments. Here you can also enter text. The value of the text is 0.

The functions MINA() and MAXA() return 0 if no value (numeric or text) and no error was encountered.

### Syntax

`MINA(Value1; Value2; ... Value30)`

Value1; Value2;...Value30 are values or ranges. Text has the value of 0.

### Example

`=MINA(1;"Text";20)` returns 0.

`=MINA(A1:B100)` returns the smallest value in the list.

## MIN

Returns the minimum value in a list of arguments.

Returns 0 if no numeric value and no error was encountered in the cell range(s) passed as cell reference(s). Text cells are ignored by MIN() and MAX(). The functions MINA() and MAXA() return 0 if no value (numeric or text) and no error was encountered. Passing a literal string argument to MIN() or MAX(), e.g. MIN("string"), still results in an error.

### Syntax

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

Number1; Number2;...Number30 are numerical values or ranges.

### Example

`=MIN(A1:B100)` returns the smallest value in the list.

## MEDIAN

Returns the median of a set of numbers. In a set containing an uneven number of values, the median will be the number in the middle of the set and in a set containing an even number of values, it will be the mean of the two values in the middle of the set.

### Syntax

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

Number1; Number2;...Number30 are values or ranges, which represent a sample. Each number can also be replaced by a reference.

### Example

for an odd number: `=MEDIAN(1;5;9;20;21)` returns 9 as the median value.

for an even number: `=MEDIAN(1;5;9;20)` returns the average of the two middle values 5 and 9, thus 7.

## MAXA

Returns the maximum value in a list of arguments. In opposite to MAX, here you can enter text. The value of the text is 0.

The functions MINA() and MAXA() return 0 if no value (numeric or text) and no error was encountered.

### Syntax

`MAXA(Value1; Value2; ... Value30)`

Value1; Value2;...Value30 are values or ranges. Text has the value of 0.

### Example

`=MAXA(A1;A2;A3;50;100;200;"Text")` returns the largest value from the list.

`=MAXA(A1:B100)` returns the largest value from the list.

## MAX

Returns the maximum value in a list of arguments.

Returns 0 if no numeric value and no error was encountered in the cell range(s) passed as cell reference(s). Text cells are ignored by MIN() and MAX(). The functions MINA() and MAXA() return 0 if no value (numeric or text) and no error was encountered. Passing a literal string argument to MIN() or MAX(), e.g. MIN("string"), still results in an error.

### Syntax

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

Number1; Number2;...Number30 are numerical values or ranges.

### Example

`=MAX(A1;A2;A3;50;100;200)` returns the largest value from the list.

`=MAX(A1:B100)` returns the largest value from the list.

## AVERAGEIFS

Returns the arithmetic mean of all cells in a range that satisfy given multiple criteria. The AVERAGEIFS function sums up all the results that match the logical tests and divides this sum by the quantity of selected values.

## AVERAGEIF

Returns the arithmetic mean of all cells in a range that satisfy a given condition. The AVERAGEIF function sums up all the results that match the logical test and divides this sum by the quantity of selected values.

## AVERAGEA

Returns the average of the arguments. The value of a text is 0.

### Syntax

`AVERAGEA(Value1; Value2; ... Value30)`

Value1; Value2;...Value30 are values or ranges. Text has the value of 0.

### Example

`=AVERAGEA(A1:A50)`

## AVERAGE

Returns the average of the arguments.

### Syntax

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

Number1; Number2;...Number30 are numerical values or ranges.

### Example

`=AVERAGE(A1:A50)`

## AVEDEV

Returns the average of the absolute deviations of data points from their mean. Displays the diffusion in a data set.

### Syntax

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

Number1, Number2,...Number30 are values or ranges that represent a sample. Each number can also be replaced by a reference.

### Example

`=AVEDEV(A1:A50)`

## Related Topics

Functions by Category