QQuestion
The following table gives the marks scored by a set of students in an examination. Calculate the mean of the distribution using the shortcut method.
| Marks | Number of students (f) |
|---|---|
| 0–10 | 3 |
| 10–20 | 8 |
| 20–30 | 14 |
| 30–40 | 9 |
| 40–50 | 4 |
| 50–60 | 2 |
ICSEClass 10MathematicsMeasures Of Central Tendency03 Mark2023 Easy
✓Answer
Take the assumed mean A = 25.
| Marks | f | x | d = x − A | fd |
|---|---|---|---|---|
| 0–10 | 3 | 5 | −20 | −60 |
| 10–20 | 8 | 15 | −10 | −80 |
| 20–30 | 14 | 25 | 0 | 0 |
| 30–40 | 9 | 35 | 10 | 90 |
| 40–50 | 4 | 45 | 20 | 80 |
| 50–60 | 2 | 55 | 30 | 60 |
⇒ Σf = 40 and Σfd = 90
⇒ Mean = A + \frac{Σfd}{Σf}
⇒ Mean = 25 + \frac{90}{40}
⇒ Mean = 25 + 2.25
Therefore, the mean is 27.25.
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