5.1.5—And use the mean and standard

For grouped data, estimate the mean with Σfx/Σf using class midpoints x, and use Σfx² to estimate variance. The result depends on treating each class as concentrated at its midpoint.

Keep a table of f, x, fx and fx², use the same units, and describe the answer as an estimate because within-class positions are unknown.

A class 10≤x<20 contributes frequency×15 to the estimated total, not frequency×10 or ×20.

Grouped-data statistics are not exact raw-data statistics; changing class widths or boundaries changes the estimate.