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Standard Deviation

The Standard Deviation is a statistical measure, that is used to identify the amount that a set of values differ (or deviate) from the average value.

For any set of values, the Standard Deviation is give by the square root of the variance. I.e.

where,

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

Related Function:

STDEV.S FunctionThe Excel STDEV.P function calculates the standard deviation of a supplied set of values.

The function is new in Excel 2010 and so is not available in earlier versions of Excel. However, the Stdev.P function is simply an updated version of the Stdevp function, which __is__ available in earlier versions of Excel.

The syntax of the Stdev.P function is:

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

where the arguments, number1, [number2], etc, are between 1 and 255 numeric values, arrays of values, or references to cells containing numbers.

Note that the Stdev.P function is used when calculating the standard deviation for an entire population. If you are calculating the standard deviation of an __sample__ population, you need to use the Stdev.S function.

See the page on Standard Deviation in Excel for a comparison of the different Excel standard deviation 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 spreadsheet on the right above spreadsheet.

The standard deviation of the three years' sales figures is calculated in cell H3 of the spreadsheet. The formula for this, (shown in the spreadsheet formula bar), is:

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

As shown in cell H3, the standard deviation for the 3 years of sales figures is calculated to be **2,484.05**.

In the example above, the arguments to the Stdev.P function are input as 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, you could add these directly into the above function as follows:

Either as individual numbers:

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

Or, as an array of numbers:

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

This gives the updated standard deviation value of **2,435.35**

For further information and examples of the Excel Stdev.P function, see the Microsoft Office website.

If you get an error from the Excel Stdev.P function this is likely to be one of the following:

Common Errors

#DIV/0! | - | Occurs if none of the values that are supplied to the function are numeric. (Note that text representations of numbers, that are supplied as a part of an array, are not recognized as numeric values by the Stdev.P function). |

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