Mathematics — Standard (041) — CBSE Class 10 board question

Let assumed mean $a = 12.5$

| Class | $f_i$ | $x_i$ | $d_i = x_i - 12.5$ | $f_i d_i$ |
|-------|--------|--------|----------------------|------------|
| 0–5 | 8 | 2.5 | –10 | –80 |
| 5–10 | 7 | 7.5 | –5 | –35 |
| 10–15 | 10 | 12.5 | 0 | 0 |
| 15–20 | 13 | 17.5 | 5 | 65 |
| 20–25 | 12 | 22.5 | 10 | 120 |
| Total | 50 | | | 70 |

Using the formula:

$$\bar{x} = a + \frac{\Sigma f_i d_i}{\Sigma f_i} = 12.5 + \frac{70}{50} = 12.5 + 1.4 = \mathbf{13.9}$$

Source: Chapter 13, Section 13.2 (Assumed Mean Method)

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• Choose $a$ as the class mark of the middle class (here 10–15, so $a = 12.5$).
• $d_i = x_i - a$: find deviation of each class mark from assumed mean.
• Formula: $\bar{x} = a + \dfrac{\Sigma f_i d_i}{\Sigma f_i}$
• Examiners award marks for: correct table (class marks, $d_i$, $f_i d_i$), correct $\Sigma f_i = 50$, $\Sigma f_i d_i = 70$, and final answer 13.9. Show all table columns clearly.