Averages and Group Weights

Overview

The arithmetic mean is the total of the observations divided by their count. This interpretation provides a reliable way to combine groups: reconstruct each group total, add the totals, and divide by the combined count.

A group with more observations contributes more weight. Consequently, taking the simple average of two group averages is valid only when the two groups have equal sizes. If one group is three times as large, its average influences the combined mean three times as much.

An average is a useful summary, but it does not describe the full distribution. Two groups can have the same mean and very different spreads. The tutorial focuses on calculating and checking the mean accurately, including the quick test that a combined average must lie between the group averages.

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• Find a Weighted Average

  Combine group averages by reconstructing totals and weighting each group by its number of observations.