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In order to calculate the average and standard deviation from aggregate data, it is necessary to have available for each group: the total of values (Σx i = SUM(x)), the number of values (N=COUNT(x)) and the total of squares of the values (Σx i 2 =SUM(x 2)) of each groups.
For example, in Microsoft Excel one must first select the entire data in the original table and then go to the Insert tab and select "Pivot Table" (or "Pivot Chart"). The user then has the option of either inserting the pivot table into an existing sheet or creating a new sheet to house the pivot table.
In some circumstances, mathematicians may calculate a mean of an infinite (or even an uncountable) set of values. This can happen when calculating the mean value of a function (). Intuitively, a mean of a function can be thought of as calculating the area under a section of a curve, and then dividing by the length of that section.
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1] ¯ = ().
See also: c:Commons:PDF to image files. Upload PDF to a free online PDF-to-Excel site. For example; here. Download the Excel file. Open it in freeware LibreOffice Calc or another spreadsheet program. If you just want one table from a long Excel page, you can select that table from the Calc page. Then copy the table to a new page in Calc.
A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles - in this case the calculation is sometimes called a time average. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly.