Grouped Data Standard Deviation Calculator

About this calculator

Grouped data arrives already sorted into class intervals with a count (frequency) for each one, rather than as a list of raw individual values — a typical example is a frequency table showing how many people fall into each age bracket. Since the exact individual values inside each class are unknown, the midpoint of each class interval stands in as the best estimate for every value in that class, and the population standard deviation and variance are then computed using those midpoints weighted by their frequencies.

This calculation is standard in introductory statistics courses precisely because so much real-world data — census age brackets, income ranges, exam score bands, histogram bins — comes pre-grouped rather than as raw individual measurements, so students and analysts need a method for estimating spread from summarized frequency-table data rather than from a full data set.

Enter the midpoint and frequency of each class, and the calculator computes the grouped population standard deviation and variance for the data set.