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

Mean Calculation (Direct Method):

| Class | $f_i$ | $x_i$ | $f_i x_i$ |
|-------|--------|--------|------------|
| 0–10 | 8 | 5 | 40 |
| 10–20 | 7 | 15 | 105 |
| 20–30 | 15 | 25 | 375 |
| 30–40 | 20 | 35 | 700 |
| 40–50 | 12 | 45 | 540 |
| 50–60 | 8 | 55 | 440 |
| 60–70 | 10 | 65 | 650 |
| Total | $\Sigma f_i = 80$ | | $\Sigma f_i x_i = 2850$ |

$$\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i} = \frac{2850}{80} = \textbf{35.625}$$

Mode Calculation:

The highest frequency is 20, corresponding to class 30–40 → Modal class = 30–40.

Here, $l = 30,\ f_1 = 20,\ f_0 = 15,\ f_2 = 12,\ h = 10$

$$\text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h = 30 + \frac{20-15}{40-15-12} \times 10$$

$$= 30 + \frac{5}{13} \times 10 = 30 + 3.846 \approx \textbf{33.85}$$

Source: Chapter 13, Sections 13.2 and 13.3

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• Mean: Use mid-points ($x_i$) of each class; apply $\bar{x} = \frac{\Sigma f_i x_i}{\Sigma f_i}$.
• Modal class: The class with the highest frequency (20 here, i.e., 30–40).
• In the mode formula, $f_0$ = frequency of class before modal class, $f_2$ = frequency of class after modal class. Don't mix these up.
• Show the full table for Mean — examiners award step marks for correct $x_i$ and $f_i x_i$ columns.
• Round mode to 2 decimal places unless told otherwise.