The Standard Deviation is a statistical measure, that is closely linked to the 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.
For any set of values, the Standard Deviation is give by the square root of the variance. ie.
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 Standard Deviation pageThe Excel STDEVPA function calculates the standard deviation of a supplied set of values.
The format of the function is :
where the arguments, number1, [number2], etc, are one or more numerical values or references to cells containing numbers.
If you are using Excel 2007 or Excel 2010, you can enter up to 255 number arguments to the function. However, in Excel 2003, the function can only accept up to 30 number arguments.
Note that the Stdevpa function is used when calculating the standard deviation for an entire population. If you are calculating the standard deviation of an sample population, you need to use the Stdev or the need to use the Stdeva function.
The Excel Stdevpa function is very similar to the Excel Stdevp function, in that both functions calculate the standard deviation of a supplied set of values, representing an entire population.
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 Stdevp function ignores the text and logical values, whereas the Stdevpa 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 Stdevp function.
STDEVP Function  STDEVPA 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 Stdevpa function used to calculate the standard deviation 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 standard deviation calculation for cells A1  A6.
Further information and examples of the Excel Stdevpa function can be found on the Microsoft Office website.
If you get an error from the Excel Stdevpa function this is most likely to be the #VALUE! error:
#VALUE!    Occurs if any values that are supplied directly to the Stdevpa function are text values that cannot be interpreted as numeric values. 