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VAR FunctionVariance & Sample Variance

The Variance is a statistical measure, that is commonly used across a set of values, to identify the amount that the values vary 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 Variance, known as the **Sample Variance**. 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 in the set.

Further details are provided on the Wikipedia Variance pageThe Excel VARA function calculates the sample variance of a supplied set of values.

The syntax of the function is:

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

Where the number arguments are values or arrays of values that provide a minimum of 2 numeric values to the function. You can enter up to 255 number arguments to the Vara function in recent versions of Excel (2007 and later), but you can only enter up to 30 number arguments in Excel 2003.

Note that the Vara function is used when calculating the variance 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 variance for an __entire__ population, you need to use the Excel Varpa function.

The Excel Vara function is very similar to the Excel Var function, in that both functions calculate the sample variance of a supplied set of values.

The difference between these two functions applies when an array of values, containing text or logical values is supplied to the function. In this case, the Var function ignores the text and logical values, whereas the Vara function assigns the value 0 to text and the values 1 or 0 to logical values.

The rules for this are shown in the table below, compared to the rules for the Var function.

VAR Function | VARA Function | |
---|---|---|

Logical values or text (including text representations of numbers), typed directly into the list of arguments | ARE counted (TRUE=1, FALSE=0) | ARE counted (TRUE=1, FALSE=0) |

Text that cannot be interpreted as a number, typed directly into the list of arguments | #VALUE! error | #VALUE! error |

Logical values, within arrays or reference arguments | Ignored | ARE counted (TRUE=1, FALSE=0) |

Text (including empty text "", text representations of numbers, or other text), within arrays or reference arguments | Ignored | Counted as zero |

Empty cells | Ignored | Ignored |

See the page on Variance in Excel for a comparison of the different Excel variance functions.

The following spreadsheet shows the Excel Vara function used to calculate the sample variance of the set of values in cells A1-A4 and in cells A1-A6.

Formulas: | Results: |

Note that, in the spreadsheet above, the function in cell B2 includes the values in cells A5 and A6. In this case, the logical value TRUE in cell A5 is treated as the value 1 and the text in cell A6 is treated as the value 0. This is shown by the example in cell B3, in which cells A1 - A4 and the values 1 and 0 give the same result as the variance calculation for cells A1 - A6.

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

If you get an error from the Excel Vara Function, this is likely to be one of the following:

Common Error

#DIV/0! | - | Occurs if fewer than 2 numeric values have been supplied to the function. |

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