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Standard Deviation

The Standard Deviation is a statistical measure, that is closely linked to the Variance. Both measures are commonly used across a set of values, to identify the amount that the values differ (or deviate) 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 the Standard Deviation, known as the
**Sample Standard Deviation**. The equation for this 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.

A full explanation can be found on the Wikipedia Standard Deviation page
STDEV & STDEV.S Functions

In Excel 2010, the STDEV function has been replaced by the STDEV.S function, which has improved accuracy.

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

The Excel STDEV function calculates the sample standard deviation of a supplied set of values.

The format of the function is :

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

where the arguments, number1, [number2], etc, are one or more numerical values or references to cells containing numbers.

If you are using Excel 2007 or Excel 2010, you can enter up to 255 number arguments to the function. However, in Excel 2003, the function can only accept up to 30 number arguments.

Note that the Stdev function is used when calculating the standard deviation 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 standard deviation of an __entire__ population, you
need to use the Stdevp function.

Note also, that the Stdev function ignores text values and logical values if these are supplied as part of an array. If you want a function that includes text and logical values in the calculation, consider using the Stdeva function.

Imagine you wanted to find out the standard deviation 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 standard deviation 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 :

=STDEV( B3:B1002, D3:D1002, F3:F1002 )

As shown in cell H3, the standard deviation in the individual heights of the sample group is 5.4 cm.

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

Either as individual numbers:

=STDEV( B3:B1002, D3:D1002, F3:F1002, 176, 177 )

Or, as an array of numbers:

=STDEV( B3:B1002, D3:D1002, F3:F1002, {176,177} )

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

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

Common Errors

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

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