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

Finding class marks and $f_i x_i$:

| Marks ($x_i$) | No. of students ($f_i$) | $f_i x_i$ |
|---|---|---|
| 5 | 12 | 60 |
| 15 | 23 | 345 |
| 25 | 34 | 850 |
| 35 | 25 | 875 |
| 45 | 6 | 270 |
| Total | 100 | 2400 |

$$\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{2400}{100} = \mathbf{24}$$

The mean marks of the students is 24.

Source: Chapter 13, Section 13.2 – Mean of Grouped Data (Direct Method)

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• Class mark = (lower limit + upper limit) ÷ 2. For 0–10, class mark = 5; for 10–20, class mark = 15, etc.
• Multiply each class mark by its frequency to get $f_i x_i$, then sum all values.
• Apply the direct method formula: $\bar{x} = \dfrac{\Sigma f_i x_i}{\Sigma f_i}$.
• Since class marks and frequencies are small, the Direct Method is the appropriate and simplest choice here.
• Always show the table clearly — examiners award marks for the working, not just the final answer.