Grouped Standard Deviation Calculator

This calculator finds the mean and standard deviation of grouped or frequency data, where instead of a list of individual values you have categories or class intervals and how often each occurs. Data often arrives summarised this way: a frequency table of exam marks grouped into bands, ages grouped into ranges, or any survey where responses are tallied by category. To find the spread of such data you cannot simply use the raw values, because you only have the groups and their counts. The standard approach uses the midpoint of each class to represent its values, weights each midpoint by its frequency, and works the mean and standard deviation from those weighted figures. This tool does exactly that. You enter the class midpoints in one box and the matching frequencies in another, in the same order, and the calculator returns the sample standard deviation, the mean, the population standard deviation, and the total number of observations. The results update as you type. Use it for statistics homework involving frequency tables, for analysing survey or grouped data, or whenever your data comes as categories with counts rather than a raw list. The mean is the sum of each midpoint times its frequency, divided by the total frequency. The standard deviation measures how spread out the data is around that mean, using the squared deviations of the midpoints weighted by frequency. The calculator gives both the sample standard deviation, which divides by one less than the total count and is used when your data is a sample, and the population version, which divides by the full count. Because midpoints stand in for the actual values within each class, grouped statistics are an approximation, very good when classes are reasonably narrow and the data is evenly spread within them.

Uses class midpoints weighted by frequency. Mean = sum(f x) / sum(f). Sample SD divides by n - 1; population SD by n. An approximation since midpoints stand in for values.