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

Finding class marks (midpoints):

| Class | $f_i$ | $x_i$ | $f_i x_i$ |
|-------|--------|--------|------------|
| 0–10 | 5 | 5 | 25 |
| 10–20 | 18 | 15 | 270 |
| 20–30 | 15 | 25 | 375 |
| 30–40 | f | 35 | 35f |
| 40–50 | 6 | 45 | 270 |
| Total | $44 + f$ | | $940 + 35f$ |

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

$$25 = \frac{940 + 35f}{44 + f}$$

$$25(44 + f) = 940 + 35f$$

$$1100 + 25f = 940 + 35f$$

$$1100 - 940 = 35f - 25f$$

$$160 = 10f$$

$$\boxed{f = 16}$$

Source: Chapter 13 – Statistics, Section 13.2 Mean of Grouped Data

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• Examiner expects: A complete table with $x_i$ and $f_i x_i$, correct substitution into the mean formula, and clear algebraic steps to isolate $f$.
• Key formula: $\bar{x} = \dfrac{\Sigma f_i x_i}{\Sigma f_i}$ (Direct Method).
• Common mistake: Forgetting to include $f$ in $\Sigma f_i$ (denominator). Both numerator and denominator must contain $f$.
• For 3 marks: 1 mark for the table, 1 mark for setting up the equation, 1 mark for correct value of $f$.