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5
How do I calculate the estimated mean of grouped data?
Given this set of data for the test marks of a class of students, find an estimate for the mean test score of the class.
To actually calculate the mean...
Total of (frequency * midpoint) column ÷ Total Frequency
765 ÷ 23 = 33.3 (1 d.p.)
Always check your answer makes sense
| Mark (m) | Number of students | Midpoint | Freq x midpoint |
| 0<m≤25 | 4 | 12.5 | 4x12.5=50 |
| 25<m≤35 | 5 | 30 | 5x30=150 |
| 35<m≤40 | 8 | 37.5 | 8x37.5=300 |
| 40<m≤45 | 5 | 42.5 | 5x42.5=212.5 |
| 45<m≤60 | 1 | 52.5 | 1x52.5=52.5 |
| Totals: | 23 | 765 |
To actually calculate the mean...
Total of (frequency * midpoint) column ÷ Total Frequency
765 ÷ 23 = 33.3 (1 d.p.)
Always check your answer makes sense
