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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:

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:

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:

- Whether the sample standard deviation or the population standard deviation is calculated;
- Whether text and the logical values, supplied as a part of an array (or stored in a supplied range of cells) are ignored or are treated as having values. Details of these differences are outlined in Table 2 below.

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.

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.

Table 1: Comparison of the Excel Standard Deviation Functions | |||

Function | Version of Excel | Population or Sample Standard Deviation | Treatment of text & logical values |
---|---|---|---|

STDEV.S | 2010 and later (new function in Excel 2010 - replaces the old STDEV function) | Sample | Ignored |

STDEV | 2003 & 2007 (kept in Excel 2010 & 2013 for compatibility, but may be discontinued in future versions of Excel) | Sample | Ignored |

STDEVA | 2003 and later | Sample | Assigned values (see Table 2) |

STDEV.P | 2010 and later (new function in Excel 2010 - replaces the old STDEVP function) | Population | Ignored |

STDEVP | 2003 & 2007 (kept in Excel 2010 & 2013 for compatibility, but may be discontinued in future versions of Excel) | Population | Ignored |

STDEVPA | 2003 and later | Population | Assigned values (see Table 2) |

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: