Grouped Data Standard Deviation Calculator
Enter the midpoint and frequency of each class in your frequency table to find the mean, variance, and standard deviation of the grouped data.
What this calculator does
When data is organized into a frequency table with classes (ranges) instead of individual values, this calculator estimates the mean, variance, and standard deviation using the midpoint of each class as a stand-in for every value in that class.
How the calculation works
The grouped mean is the sum of each midpoint multiplied by its frequency, divided by the total frequency: mean = Σ(f·x) / Σf. The variance is the sum of each frequency multiplied by the squared deviation of its midpoint from the mean, divided by the total frequency (population) or the total frequency minus one (sample): variance = Σf(x – mean)² / N. The standard deviation is the square root of the variance.
Leave a class’s midpoint and frequency blank together to exclude it from the calculation. Because grouped data uses midpoints as approximations, results are estimates of the true underlying spread rather than exact values.