VARPA
The VARPA function returns the population (true) variance — a measure of dispersion — of a set of any values.
VARPA(value, value…)
value: Any value. value can contain a single value or collection. All values must be of the same value type (except that string values and boolean values can be included with number values). A minimum of two values are required. A string value can be included in a referenced cell, but can’t be directly entered as an argument to the function.
value…: Optionally include one or more additional values or collections of values.
Notes
The VARPA function finds the population, or true, variance (as opposed to the sample, or unbiased, variance) by dividing the sum of the squares of the deviations of the data points.
It is appropriate to use VARPA when the specified values represent the entire collection or population. If the values you are analysing represent only a sample of a larger population, use the VARA function.
The function assigns a value of 0 to any string value, 0 to the boolean value FALSE, and 1 to the boolean value TRUE and includes them in the computation, if all other values are numbers. If there are date/time values or duration values included, the function returns an error. Empty cells are ignored.
The square root of the variance returned by the VARPA function is returned by the STDEVPA function.
Example |
|---|
Suppose you installed a temperature sensor in a house in California. The sensor records each day’s high and low temperatures. The data from the first few days of July is shown in the following table and is used as a sample for the population of high and low temperatures (note that this is an example only; this would not be statistically valid). On July 5, the sensor failed, so the data in the table shows n/a, or not available. |
A | B | C | |
|---|---|---|---|
1 | Date | High | Low |
2 | 01/07/2010 | 58 | 58 |
3 | 02/07/2010 | 84 | 61 |
4 | 03/07/2010 | 82 | 59 |
5 | 04/07/2010 | 78 | 55 |
6 | 05/07/2010 | n/a | n/a |
7 | 06/07/2010 | 81 | 57 |
8 | 07/07/2010 | 93 | 67 |
=VARPA(B2:B8) returns approximately 867.142857142857, the dispersion (variance is a measure of dispersion) as measured by VARPA, of the sample of daily high temperatures. It exceeds the actual range of high temperatures because the “n/a” temperature is given a value of zero. If you had a large data set that could not easily be visually scanned, or you wished to automate checking for missing values, you could compare the results of =VARP(B2:B8), which returns approximately 112.5555555555556, with VARPA, which returns approximately 867.142857142857. If (as in this case) they are not equal, it would indicate the data set contains text (such as “n/a”), or one or more boolean values (TRUE or FALSE). |