In a test, the marks obtained by 100 students (out of 50) are given below:
| Marks obtained | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 |
|---|---|---|---|---|---|
| Number of students | 12 | 23 | 34 | 25 | 6 |
Find the mean marks of the students.
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
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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Explanation
- 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.