Estimating the mean from grouped data

Set up a grouped frequency table, work out the estimated mean using midpoints, then reveal the actual data behind the table and compare your estimate with the true mean. See also Mean estimation simulation for a visual histogram version.

Set up your frequency table

Choose how many groups you want, set the class intervals and frequencies, then generate a hidden dataset that matches your table.

Number of groups

First lower bound

Class width

Class interval	Lower bound	Upper bound	Frequency
Total frequency			0

Estimate the mean

Use midpoints and frequencies to estimate the mean. The actual raw data values are hidden until you choose to reveal them.

Class interval	Frequency (f)	Midpoint (x)	f × x
Totals		—	—

Estimated mean = Σ(f × midpoint) ÷ Σf

Your total of f × midpoint

Your estimated mean

How it works

Set class intervals and a different frequency for each group.
Generate hidden data — the tool creates real values that fall inside each class.
Work out midpoints, multiply by frequency, and divide by total frequency.
Check your estimate, then reveal the actual data to see how close your estimate is to the true mean.

The percentage difference is |estimated mean − actual mean| ÷ actual mean × 100%.

Estimating the mean from grouped data

Set up your frequency table

Estimate the mean

Comparison

Actual data values

How it works