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

Using the Direct Method:

| Daily Expenditure (₹) | $f_i$ | $x_i$ (Class Mark) | $f_i x_i$ |
|---|---|---|---|
| 100 – 120 | 8 | 110 | 880 |
| 120 – 140 | 3 | 130 | 390 |
| 140 – 160 | 8 | 150 | 1200 |
| 160 – 180 | 6 | 170 | 1020 |
| 180 – 200 | 5 | 190 | 950 |
| Total | 30 | | 4440 |

$$\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{4440}{30} = \textbf{₹148}$$

The mean daily expenditure of the employees is ₹148.

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

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• Class mark $x_i = \dfrac{\text{Upper limit} + \text{Lower limit}}{2}$ is used to represent each class interval.
• The Direct Method formula is $\bar{x} = \dfrac{\Sigma f_i x_i}{\Sigma f_i}$.
• Always show the table with all columns — examiners award marks for the working, not just the final answer.
• Verify: $\Sigma f_i = 30$ ✓ (matches total employees given in the question).