Calculating Standard Deviation In Excel

Sample and Population Standard Deviations

Excel provides functions for calculating both the Population Standard Deviation and the Sample Standard Deviation.

The Population Standard Deviation is used for a set of values representing an entire population and is calculated by the following equation:

Population Standard Deviation Equation

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.

When your data set is a sample of a population, (rather than an entire population), you should use the slightly modified form of the Standard Deviation, known as the Sample Standard Deviation. The equation for this is:

Sample Standard Deviation Equation

There are a total of six different built-in functions for calculating standard deviation in Excel. The main differences between the Excel standard deviation functions are:

Also, when Excel 2010 was released, two of the existing standard deviation functions were renamed. However, in order to maintain compatibility with older versions, Excel 2010 and Excel 2013 have also kept the old named functions.


Comparison of Functions for Calculating Standard Deviation in Excel

Table 1 (below) provides a description of the different types of standard deviation function. This will help you to decide which of the functions should be used when calculating a standard deviation in Excel.

Selecting a function name will take you to a full description of the function, with examples of use.



STDEV.S vs. STDEVA and STDEV.P vs. STDEVPA

The STDEV.S and STDEVA functions, and the STDEV.P and STDEVPA differ only in the way they handle text and logical values that are supplied as a part of an array or range of cells.

For example, if a range of cells containing the logical value TRUE is supplied to the STDEV function, this will return a different result to the same range of cells supplied to the STDEVA function.

The treatment of text and logical values supplied to the standard deviation functions is summarised in the following table: