When data is grouped, such as times 0 < t ≤ 5, 5 < t ≤ 10, we do not know the exact values. To estimate the mean, use the midpoint of each group as if every value were there.
Multiply each midpoint by its frequency, add these products, then divide by the total frequency. The modal class is the group with the highest frequency. The answer is an estimate, because the real values could be anywhere in each group.
Worked example
Groups 0–10 (frequency 4) and 10–20 (frequency 6). Estimate the mean.
- Midpoints 5 and 15: 5 × 4 + 15 × 6 = 20 + 90 = 110.
- Total frequency 10: 110 ÷ 10 = 11.
Answer:11
Key words
- frequency
- how many values are in a group
- midpoint
- the middle of a group
- modal class
- the group with the highest frequency
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