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.
For any set of values, the equation for calculating the Variance 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.
A full explanation can be found on the Wikipedia Variance pageThe Excel VARPA function returns the Variance of a given set of values.
The format of the function is :
Where the number arguments provide a minimum of 2 numerical values to the function. You can enter up to 254 number arguments to the Varpa function in Excel 2007 or Excel 2010, but you can only enter up to 30 number arguments in Excel 2003.
Note that the Varpa function is used when calculating the variance of a whole population. If your data is just a sample of the population (eg. if your data set records the individual heights of a sample of UK males), you need to use the Excel Vara function.
The Excel Varpa function is very similar to the Excel Varp function, in that both functions calculate the 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 Varp function ignores the text and logical values, whereas the Varpa 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 Varp function.
VARP Function  VARPA 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 
The following spreadsheet shows the Excel Varpa function used to calculate the variance of the set of values in cells A1A4 and in cells A1A6.
The format of the functions are shown in the spreadsheet on the left and the resulting values are shown in the spreadsheet on the right.
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 Varpa function can be found on the Microsoft Office website.
If you get an error from the Excel Varpa Function, this is likely to be the #DIV/0! error:
#DIV/0!    Occurs if fewer than 2 numerical values have been supplied to the function 