How to use this grouped data mean calculator
Enter your class intervals (like 0-10, 10-20) in the first box and their frequencies in the second, in matching order, then press Calculate. The table shows each class's midpoint and f × x contribution, so the estimate is fully auditable.
Why grouped data needs a special mean
Once data has been summarised into a frequency table, the original values are gone. We know eight students scored "20–30" but not their exact marks. The grouped mean proceeds on one honest assumption: pretend every value sits at its class midpoint. The result is an estimate, usually a good one, and statistics is upfront about that.
Marks distribution: classes 0–10 (f = 2), 10–20 (f = 5), 20–30 (f = 8), 30–40 (f = 3). Midpoints 5, 15, 25, 35 give Σfx = 10 + 75 + 200 + 105 = 390 over 18 students: estimated mean ≈ 21.7 marks. The true mean of the lost raw scores would be close. Closeness improves as classes narrow.
How accurate is the estimate?
It depends on how values truly distribute inside each class. If they cluster at the bottom of each interval, the midpoint method overestimates; at the top, it underestimates; spread evenly, and the errors largely cancel. Narrower classes mean smaller possible error. That is why serious grouped tables use many classes, and why raw data, when you can keep it, is always better.
Frequently asked questions
Why is the grouped mean only an estimate?
Because the original values are lost in the grouping. Assuming each sits at its class midpoint approximates the true mean, with accuracy improving as classes get narrower.
What is a class midpoint?
The average of a class interval's endpoints: for 20–30 it is 25. It represents every value in that class in the calculation.
Can I calculate a grouped median or mode?
Yes. Grouped formulas exist for both, using cumulative frequencies (median) and the modal class (mode). They are separate estimators with their own pages planned on this site.