Estimating Mean from Grouped Data

Overview

This lecture explains how to estimate the mean from grouped frequency tables by calculating midpoints, products, and using a formula.

Create two extra columns: one for midpoints of each group, one for frequency × midpoint.
Calculate the midpoint for each class interval (e.g., (0+10)/2 = 5).
Multiply each midpoint by its class frequency to get frequency × midpoint values.
Add up all frequencies to find the total number of data points.
Add up all frequency × midpoint values to get the total sum.
Divide the total frequency × midpoint sum by the total frequency to estimate the mean.
Round the final answer appropriately based on standard rounding rules.

Example class intervals and frequencies: 0–10 (7), 10–30 (11), ..., 100–120 (3).
Sample midpoints: 0–10 = 5, 10–30 = 20, ..., 100–120 = 110.
Example products: 7×5=35, 11×20=220, ..., 3×110=330.
Example totals: frequencies sum to 80; frequency × midpoint totals to 4,235.
Divide 4,235 by 80 to get 52.9375; round to 52.94.

Grouped Frequency Table — A table showing data grouped into intervals (classes) with their frequencies.
Midpoint — The average of the lower and upper boundaries of a class interval.
Frequency — The number of data points in each group.
Estimated Mean — The mean value calculated using midpoints and frequencies in grouped data.