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VAR 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, 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.

VARP and VAR.P

In Excel 2010, the VARP function has been replaced by the VAR.P, which has improved accuracy.

Although it has been replaced, the Varp function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.

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

The syntax of the function is:

VARP( number1, [number2], ... )

Where the number arguments are values or arrays of values that provide a minimum of 2 numeric values to the function. You can enter up to 254 number arguments to the Varp function in current versions of Excel (Excel 2007 and later. However, you can only enter up to 30 number arguments in Excel 2003.

Note that the Varp 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 Excel Var or the Excel 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:

=VARP( 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 Varp 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 2012 the sales figures are 13,000 and 14,500 we can add these directly into the above function as follows:

Either as individual numbers:

=VARP( B3:B14, D3:D14, F3:F14, 13000, 14500 )

or, as an array of numbers:

=VARP( 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 Varp function are provided on the Microsoft Office website.

If you get an error from the Excel Varp 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 Varp function are text values that cannot be interpreted as numeric values. |