Grouped Data Mean Calculator

Work out grouped data mean instantly with clear inputs, formula shown and shareable results.

About Grouped Data Mean Calculator

For grouped data the individual values are unknown, so each class is represented by its midpoint. The mean is then Σfx / Σf, which is exact only if the values are evenly spread within each class.

Formula

Grouped mean

x̄ = Σ(f·x) / Σf, using class midpoints for x

Worked example

With the default values below, Grouped Data Mean Calculator returns Mean of the grouped data of 25.25000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Class midpoints: 5, 15, 25, 35, 45
Class frequencies: 4, 8, 15, 9, 4

Results

Mean of the grouped data: 25.25000000
Standard deviation: 11.20611097
Total frequency: 40
Σfx: 1,010.000000

Step by step

1Values used
2Grouped mean
3Mean of the grouped data= 25.25000000
4Standard deviation= 11.20611097
5Total frequency= 40
6Σfx= 1,010.000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or fees or charges into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For midpoints 5–45 with frequencies 4, 8, 15, 9, 4?

Σf = 40 and Σfx = 20 + 120 + 375 + 315 + 180 = 1010, so the mean is 25.25.

Why is it only an estimate?

Because using the midpoint assumes symmetry within each class; skew inside a class biases the result.