NumericalModerate3 marks
Calculate the mean of the following distribution using step deviation method.
Topic: Mean / median / mode / quartiles
Previous-year question practice database
Answer
Solution diagram
Exam answer
| Marks | f | Class mark x | u=(x−35)/10 | fu |
|---|---|---|---|---|
| 0–10 | 10 | 5 | −3 | −30 |
| 10–20 | 9 | 15 | −2 | −18 |
| 20–30 | 25 | 25 | −1 | −25 |
| 30–40 | 30 | 35 | 0 | 0 |
| 40–50 | 16 | 45 | 1 | 16 |
| 50–60 | 10 | 55 | 2 | 20 |
| Total | Σf=100 | Σfu=−37 |
A = 35, h = 10.
Mean = A + h(Σfu/Σf) = 35 + 10(−37/100) = 31.3.
Answer: 31.3 marks.
Explanation
Use the step-deviation formula x̄ = A + hΣfu/Σf.
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