# Statistical Functions Part Four

## 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.

## 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.

## AVEDEV

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

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

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

=AVEDEV(A1:A50)

## AVERAGE

Returns the average of the arguments.

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

Number1, Number2, ..., Number30 are numeric values or ranges.

=AVERAGE(A1:A50)

## AVERAGEA

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

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

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

=AVERAGEA(A1:A50)

## 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.

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

Number1, Number2, ..., Number30 are numeric values or ranges.

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

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

## MAXA

Returns the maximum value in a list of arguments. Unlike MAX, you can also use text strings. The value of a text string is 0.

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

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

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

=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.

## 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.

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

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

for an odd number: =MEDIAN(1;5;9;20;21) returns the middle value, 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, i.e. 7.

## 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.

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

Number1, Number2, ..., Number30 are numeric values or ranges.

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

## MINA

Returns the minimum value in a list of arguments. Unlike MIN, you can also use text strings. The value of a text string is 0.

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

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

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

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

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

## 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.

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

Number1, Number2, ..., Number30 are numeric values or ranges.

=MODE(A1:A50)

## MODE.MULT

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

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

Number1, Number2, ..., Number30 are numeric 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.

=MODE.MULT(A1:A50)

## 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.

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

Number1, Number2, ..., Number30 are numeric values or ranges.

If the data set contains no duplicate data points, MODE.SNGL returns the #VALUE! error value.

=MODE.SNGL(A1:A50)

## NEGBINOM.DIST

Returns the negative binomial density or distribution function.

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

X is the value returned for unsuccessful tests.

R is 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.

=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.

NEGBINOMDIST(X; R; SP)

X is the value returned for unsuccessful tests.

R is the value returned for successful tests.

SP is the probability of the success of an attempt.

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

## NORM.DIST

Returns the density function or the normal cumulative distribution.

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.

StandardDeviation is the standard deviation of the distribution.

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

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

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

## NORM.INV

Returns the inverse of the normal cumulative distribution.

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.

=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.

## NORMDIST

Returns the normal density function or the normal cumulative distribution function.

NORMDIST(Number; Mean; StandardDeviation; 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.

StandardDeviation is the standard deviation of the distribution.

C (optional). C = 0 calculates the density function, C = 1 calculates the cumulative distribution function.

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

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

## NORMINV

Returns the inverse of the normal cumulative distribution.

NORMINV(Number; Mean; StandardDeviation)

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

Mean is the mean value in the normal distribution.

StandardDeviation is the standard deviation of the normal distribution.

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

## PEARSON

Returns the Pearson product moment correlation coefficient r.

PEARSON(Data1; Data2)

Data1 is the array of the first data set.

Data2 is the array of the second data set.

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

## 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 yields the first quartile; Alpha = 50% is the MEDIAN.

PERCENTILE(Data; Alpha)

Data is the array of data.

Alpha is the percentage of the scale between 0.0 and 1.0.

=PERCENTILE(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 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.

PERCENTILE.EXC(Data; Alpha)

Data is the array of data.

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

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

## 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 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.

PERCENTILE.INC(Data; Alpha)

Data is the array of data.

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

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

## PERCENTRANK

Returns the percentage rank of a value in a sample.

PERCENTRANK(Data; Value; Significance)

Data is the array of data in the sample.

Value is the value for which the percentile rank must be determined.

Significance An optional argument that specifies the number of significant digits that the returned percentage value is rounded to. If omitted, a value of 3 is used.

=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.

## 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.

PERCENTRANK.EXC(Data; Value; Significance)

Data is 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.

=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.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.

PERCENTRANK.INC(Data; Value; Significance)

Data is 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.

=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.

## PHI

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

PHI(Number)

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

=PHI(2.25) = 0.03

=PHI(-2.25) = 0.03

=PHI(0) = 0.4

## POISSON

Returns the Poisson distribution.

POISSON(Number; Mean; C)

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

Mean is 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.

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

## POISSON.DIST

Returns the Poisson distribution.

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.

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

## QUARTILE

Returns the quartile of a data set.

QUARTILE(Data; Type)

Data is the array of data in the sample.

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

=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.

## 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.

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)

=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.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.

QUARTILE.INC(Data; Type)

Data is 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.)

=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.