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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 5 · Set 3 · Q33
(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 : $\displaystyle 12$ $\displaystyle 15$ $\displaystyle 20$ $\displaystyle 16$ $\displaystyle 10$ $\displaystyle 16$ $\displaystyle 11$
(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 |
| $\displaystyle 60$-$\displaystyle 80$ | $\displaystyle 70$ | $\displaystyle 28$ | $\displaystyle 1960$ |
| $\displaystyle 80$-$\displaystyle 100$ | $\displaystyle 90$ | $\displaystyle 13$ | $\displaystyle 1170$ |
| $\displaystyle 68+\mathrm{p}$ | $\displaystyle 3700+50 p$ |
OR
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 | $\displaystyle c f$ |
| $\displaystyle 115$ | $\displaystyle 110$-$\displaystyle 120$ | $\displaystyle 12$ | $\displaystyle 12$ |
| $\displaystyle 125$ | $\displaystyle 120$-$\displaystyle 130$ | $\displaystyle 15$ | $\displaystyle 27$ |
| $\displaystyle 135$ | $\displaystyle 130$-$\displaystyle 140$ | $\displaystyle 20$ | $\displaystyle 47$ |
| $\displaystyle 145$ | $\displaystyle 140$-$\displaystyle 150$ | $\displaystyle 16$ | $\displaystyle 63$ |
| $\displaystyle 155$ | $\displaystyle 150$-$\displaystyle 160$ | $\displaystyle 10$ | $\displaystyle 73$ |
| $\displaystyle 165$ | $\displaystyle 160$-$\displaystyle 170$ | $\displaystyle 16$ | $\displaystyle 89$ |
| $\displaystyle 175$ | $\displaystyle 170$-$\displaystyle 180$ | $\displaystyle 11$ | $\displaystyle 100$ |
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CBSE Class 10 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.