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VAR.S FunctionVariance

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.

For any set of values, x, the equation for calculating the Variance is:

where,

- x takes on each value in the set;
- x is the average of the set of values;
- n is the number of values.

The Excel VAR.P function returns the Variance of a given set of values.

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

The syntax of the Var.P function is:

VAR.P( number1, [number2], ... )

Where the number arguments are values or arrays of values that provide a minimum of 2 numeric values to the function. The maximum number of arguments that can be supplied to the VAR.P function is 254.

Note that the Var.P function is used when calculating the variance of an entire population. If your data is just a __ sample__ of the population (e.g. if your data set records the individual heights of a sample of UK males), you should use the Var.S function.

See the page on Variance in Excel for a comparison of the different Excel variance functions.

A company keeps a record of its monthly sales figures, over the last three years. These are stored in cells B3-B14, D3-D14 and F3-F14 of the above example spreadsheet on the right.

The variance of the three years' sales figures is calculated in cell H3 of the spreadsheet. The formula for this, as shown in the formula bar, is:

=VAR.P( B3:B14, D3:D14, F3:F14 )

As shown in cell H3, the variance for the 3 years of sales figures is *6,170,524.69*.

The example above shows the arguments to the Var.P 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, during January and February 2010 the sales figures are 13,000 and 14,500 we can add these directly into the above function as follows:

Either as individual numbers:

=VAR.P( B3:B14, D3:D14, F3:F14, 13000, 14500 )

or, as an array of numbers:

=VAR.P( B3:B14, D3:D14, F3:F14, {13000,14500} )

This gives the updated variance of *5,930,921.05*.

Further details and examples of the Excel Var.P function are provided on the Microsoft Office website.

If you get an error from the Excel Var.P Function, this is likely to be one of the following:

Common Errors

#DIV/0! | - | Occurs if none of the values that have been supplied to the function are numeric. |

#VALUE! | - | Occurs if any values that are supplied directly to the Var.P function are text values that cannot be interpreted as numeric values. |