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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 (statistical mean) of the set of values, and n is the number of values in the set.

A full explanation can be found on the Wikipedia Variance pageVARP 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In Excel 2010, the VARP function has been replaced by the VAR.P, which has improved accuracy.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 provide a minimum of 2 numerical values to the function. You can enter up to 254 number arguments to the Varp function in Excel 2007 and later versions of Excel, but 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 (eg. if your data set records the individual heights of a sample of UK males), you need to use the Excel Var or the Excel Var.S function.

Note also, that the Varp 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 population variance function that does not ignore text and logical values that are supplied as a part of an array, consider using the Varpa function.

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 information and examples of the Excel Varp function can be found on the Microsoft Office website.

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

Common Errors

#DIV/0! | - | Occurs if fewer than 2 numerical values have been supplied to the function. |