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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 5 · Set 3 · Q33
(a) The mean of the following distribution is 53. Find the missing frequency p. Class Interval: 0-20 20-40 40-60 60-80 80-100 Frequency: 1215 p 2813…
(a)
The mean of the following distribution is $\displaystyle 53$ . Find the missing frequency p. Class Interval : $\displaystyle 0$-$\displaystyle 20$ $\displaystyle 20$-$\displaystyle 40$ $\displaystyle 40$-$\displaystyle 60$ $\displaystyle 60$-$\displaystyle 80$ $\displaystyle 80$-$\displaystyle 100$ Frequency : $\displaystyle 1215$ p $\displaystyle 2813$ Hence, find mode of the distribution.
(b)
Compute median of the following data :
| Mid-value : | $\displaystyle 115$ | $\displaystyle 125$ | $\displaystyle 135$ | $\displaystyle 145$ | $\displaystyle 155$ | $\displaystyle 165$ | $\displaystyle 175$ |
| Frequency : | $\displaystyle 12$ | $\displaystyle 15$ | $\displaystyle 20$ | $\displaystyle 16$ | $\displaystyle 10$ | $\displaystyle 16$ | $\displaystyle 11$ |
Marking-scheme solution
| Class Interval | $\displaystyle x_{i}$ | $\displaystyle f_{i}$ | $\displaystyle f_{i} x_{i}$ |
| $\displaystyle 0$-$\displaystyle 20$ | $\displaystyle 10$ | $\displaystyle 12$ | $\displaystyle 120$ |
| $\displaystyle 20$-$\displaystyle 40$ | $\displaystyle 30$ | $\displaystyle 15$ | $\displaystyle 450$ |
| $\displaystyle 40$-$\displaystyle 60$ | $\displaystyle 50$ | p | 50p |
| $\displaystyle 60$-$\displaystyle 80$ | $\displaystyle 70$ | $\displaystyle 28$ | $\displaystyle 1960$ |
| $\displaystyle 80$-$\displaystyle 100$ | $\displaystyle 90$ | $\displaystyle 13$ | $\displaystyle 1170$ |
| $\displaystyle 68+\mathrm{p}$ | $\displaystyle 3700+50 p$ |
Mean $\displaystyle =53=\frac{3700+50 \mathrm{p}}{68+\mathrm{p}}$
$\displaystyle \Rightarrow \mathrm{p}=32$
Modal class is $\displaystyle 40-60$
\[\begin{aligned}
\text { Mode } & =40+\frac{32-15}{64-15-28} \times 20 \\
& =\frac{1180}{21} \text { or } 56.1 \text { (approx.) }
\end{aligned}
\]
Mid-value : $\displaystyle \begin{array}{lllllll}115 & 125 & 135 & 145 & 155 & 165 & 175\end{array}$
Frequency : $\displaystyle \begin{array}{lllllll}12 & 15 & 20 & 16 & 10 & 16 & 11\end{array}$
| Mid-Value | Class Interval | f | $\displaystyle c f$ |
| $\displaystyle 115$ | $\displaystyle 110$-$\displaystyle 120$ | $\displaystyle 12$ | $\displaystyle 12$ |
| $\displaystyle 125$ | $\displaystyle 120$-$\displaystyle 130$ | $\displaystyle 15$ | $\displaystyle 27$ |
| $\displaystyle 135$ | $\displaystyle 130$-$\displaystyle 140$ | $\displaystyle 20$ | $\displaystyle 47$ |
| $\displaystyle 145$ | $\displaystyle 140$-$\displaystyle 150$ | $\displaystyle 16$ | $\displaystyle 63$ |
| $\displaystyle 155$ | $\displaystyle 150$-$\displaystyle 160$ | $\displaystyle 10$ | $\displaystyle 73$ |
| $\displaystyle 165$ | $\displaystyle 160$-$\displaystyle 170$ | $\displaystyle 16$ | $\displaystyle 89$ |
| $\displaystyle 175$ | $\displaystyle 170$-$\displaystyle 180$ | $\displaystyle 11$ | $\displaystyle 100$ |
$\displaystyle \begin{aligned} \frac{100}{2}=50 & \text {, Median class is } 140-150 \\ \text { Median } & =140+\frac{50-47}{16} \times 10 \\ & =\frac{1135}{8} \text { or } 141.8 \text { (approx.) }\end{aligned}$
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.