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

Using the Direct Method: $\bar{x} = \dfrac{\Sigma f_i x_i}{\Sigma f_i}$

| Classes | $f_i$ | $x_i$ (class mark) | $f_i x_i$ |
|---------|-------|---------------------|-----------|
| 25–30 | 14 | 27.5 | 385.0 |
| 30–35 | 22 | 32.5 | 715.0 |
| 35–40 | 16 | 37.5 | 600.0 |
| 40–45 | 6 | 42.5 | 255.0 |
| 45–50 | 5 | 47.5 | 237.5 |
| 50–55 | 3 | 52.5 | 157.5 |
| 55–60 | 4 | 57.5 | 230.0 |
| Total | 70 | | 2580.0 |

$$\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{2580}{70} = \mathbf{36.86}$$

The mean of the distribution is 36.86 (approx).

Source: Chapter 13, Section 13.2 Mean of Grouped Data

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• Class mark $x_i$ = (lower limit + upper limit) / 2 for each class. Always write this column clearly.
• Use the Direct Method here since the values are small and manageable.
• $\Sigma f_i = 70$ is the total frequency — verify this first to avoid errors.
• Examiner awards marks for: correct class marks, correct $f_i x_i$ products, correct $\Sigma f_i x_i$, and correct final division. Show each step.