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STDEV.P FunctionStandard Deviation

Standard Deviation is a statistical measure, that is closely linked to 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;
- n is the number of values.

Further information is provided on the Wikipedia Standard Deviation page

The Excel STDEV.S function calculates the sample 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.S function is simply an updated version of the Stdev function, which __is__ available in earlier versions of Excel.

The syntax of the Stdev.S function is:

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

where the arguments, number1, [number2], etc, are between 1 and 255 numeric values, arrays of values, or references to cells containing numbers. The supplied arguments must provide at least two numeric values to the function.

Note that the Stdev.S function is used when calculating the standard deviation for a __sample__ of a population (e.g. 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 should use the Stdev.P function.

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

Imagine you wanted to find out the standard deviation of the heights of adult males in London. It is not possible to measure the height of __all__ males, but you could take a sample of the population and measure their heights.

The above 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 spreadsheet formula bar, is:

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

As shown in cell H3, the Stdev.S function calculates the standard deviation in the measured heights to be **5.4 cm**.

In the example above, the arguments to the Stdev.S 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.S( B3:B1002, D3:D1002, F3:F1002, 176, 177 )

Or, as an additional array of numbers:

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

Further information and examples of the Excel Stdev.S function are provided on the Microsoft Office website.

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

Common Errors

#DIV/0! | - | Occurs if fewer than two numeric values are supplied to the function. (Note that text representations of numbers, that are supplied as a part of an array, are not interpreted as numeric values by the Stdev.S function) |

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