The Excel VAR.S Function

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Related Function:  VAR.P Function

Variance & Sample Variance

The Variance is a statistical measure, that is commonly used across a set of values, to identify the amount that the values vary from the average value.

When your data set is a sample of a population, (rather than an entire population), you should use a slightly modified form of Variance, known as the Sample Variance. The equation for this is :

where x is the average (statistical mean) of the set of values, and n is the number of values.

A full explanation can be found on the Wikipedia Variance page (link opens in a new window)

Basic Description

The Excel VAR.S function calculates the sample variance of a supplied set of values.

The VAR.S function is new to Excel 2010. However, this is simply an improved (slightly more accurate) version of the VAR function, which is available in earlier versions of Excel.

The format of the function is :

Where the number arguments are up to 254 values or arrays of values. You must provide a minimum of 2 values to the function.

Note that the Var.S function is used when calculating the variance for a sample of a population (eg. if your data set records the individual heights of a sample of UK males). If you are calculating the variance for an entire population, you need to use the Excel Var.P function.

Note also, that the Var.S function ignores text values and logical values if these are supplied as part of an array. However, if they are supplied directly to the function, text representations of numbers and logical values are interpreted as numbers. If you want a sample variance functon that does not ignore text and logical values that are supplied as a part of an array, consider using the Vara function.

Var.S Function Example

Imagine you wanted to find out the variance of the heights of adult males in London. It is not realistic to measure the height of all males, but you could take a sample of the population and measure their heights.

The example spreadsheet on the right stores the measurements (in cm) of 3,000 adult males. The measured heights are stored in cells B3 - B1002, D3 - D1002 and F3 - F1002.

The variance of the heights of the sample group is calculated in cell H3 of the spreadsheet. The formula for this, as shown in the formula bar, is :

As shown in cell H3, the variance of the individual heights of the sample group is 9.261904762 cm.

Other Argument Types

The example above shows the arguments to the Var.S function being input in the form of 3 cell ranges. However, you can also input figures directly, as individual numbers or number arrays.

For example, if you wanted to include two further heights, of 176cm and 177cm into the sample we could add these directly into the above function as follows:

Either as individual numbers:

Or, as an array of numbers:

Further information and examples of the Excel Var.S function can be found on the Microsoft Office website.

Trouble Shooting

If you get an error from the Excel Var.S Function, this is likely to be the #DIV/0! error:

Some users may also encounter the following problem with the Var.S function: