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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 5 · Set 2 · Q35
(a) Find the mean and mode of the following frequency distribution: Class Interval: 400-450 450-500 500-550 550-600 600-650 650-700 Frequency:…
Find the mean and mode of the following frequency distribution : Class Interval : $\displaystyle 400$-$\displaystyle 450$ $\displaystyle 450$-$\displaystyle 500$ $\displaystyle 500$-$\displaystyle 550$ $\displaystyle 550$-$\displaystyle 600$ $\displaystyle 600$-$\displaystyle 650$ $\displaystyle 650$-$\displaystyle 700$ Frequency : $\displaystyle 151820232212$
If the median of the following frequency distribution is $\displaystyle 32.5$ and sum of all frequencies is $\displaystyle 40$, then find the values of $\displaystyle \mathrm{f}_{1}$ and $\displaystyle \mathrm{f}_{2}$ : Class Interval : $\displaystyle 0$-$\displaystyle 10$ $\displaystyle 10$-$\displaystyle 20$ $\displaystyle 20$-$\displaystyle 30$ $\displaystyle 30$-$\displaystyle 40$ $\displaystyle 40$-$\displaystyle 50$ $\displaystyle 50$-$\displaystyle 60$ $\displaystyle 60$-$\displaystyle 70$ Frequency: $\displaystyle \begin{array}{llllllll}\mathrm{f}_{1} & 9 & 12 & 6 & \mathrm{f}_{2} & 2\end{array}$
Marking-scheme solution
Class Interval & $\displaystyle x_{i}$ & $\displaystyle f_{i}$ & $\displaystyle u_{i}=\frac{x_{i}-525}{50}$ & $\displaystyle f_{i} u_{i}$
$\displaystyle 400$-$\displaystyle 450$ & $\displaystyle 425$ & $\displaystyle 15$ & -$\displaystyle 2$ & -$\displaystyle 30$
$\displaystyle 450$-$\displaystyle 500$ & $\displaystyle 475$ & $\displaystyle 18$ & -$\displaystyle 1$ & -$\displaystyle 18$
$\displaystyle 500$-$\displaystyle 550$ & $\displaystyle 525$ & $\displaystyle 20$ & $\displaystyle 0$ & $\displaystyle 0$
$\displaystyle 550$-$\displaystyle 600$ & $\displaystyle 575$ & $\displaystyle 23$ & $\displaystyle 1$ & $\displaystyle 23$
$\displaystyle 600$-$\displaystyle 650$ & $\displaystyle 625$ & $\displaystyle 22$ & $\displaystyle 2$ & $\displaystyle 44$
$\displaystyle 650$-$\displaystyle 700$ & $\displaystyle 675$ & $\displaystyle 12$ & $\displaystyle 3$ & $\displaystyle 36$
& & $\displaystyle 110$ & & $\displaystyle 55$
\[\begin{aligned}
\text { Mean } & =525+\frac{55}{110} \times 50
& =550
\end{aligned}
\]
Modal class is $\displaystyle 550$-$\displaystyle 600$
\[\begin{aligned}
\text { Mode } & =550+\frac{23-20}{46-20-22} \times 50
& =\frac{1175}{2}=587.5
\end{aligned}
\]
Frequency : & $\displaystyle 3$ & $\displaystyle \mathrm{f}_{1}$ & $\displaystyle 9$ & $\displaystyle 12$ & $\displaystyle 6$ & $\displaystyle \mathrm{f}_{2}$ & $\displaystyle 2$
Class Interval & f & $\displaystyle c f$
$\displaystyle 0$-$\displaystyle 10$ & $\displaystyle 3$ & $\displaystyle 3$
$\displaystyle 10$-$\displaystyle 20$ & $\displaystyle \mathrm{f}_{1}$ & $\displaystyle 3+\mathrm{f}_{1}$
$\displaystyle 20$-$\displaystyle 30$ & $\displaystyle 9$ & $\displaystyle 12+\mathrm{f}_{1}$
$\displaystyle 30$-$\displaystyle 40$ & $\displaystyle 12$ & $\displaystyle 24+\mathrm{f}_{1}$
$\displaystyle 40$-$\displaystyle 50$ & $\displaystyle 6$ & $\displaystyle 30+\mathrm{f}_{1}$
$\displaystyle 50$-$\displaystyle 60$ & $\displaystyle \mathrm{f}_{2}$ & $\displaystyle 30+\mathrm{f}_{1}+\mathrm{f}_{2}$
$\displaystyle 60$-$\displaystyle 70$ & $\displaystyle 2$ & $\displaystyle 32+\mathrm{f}_{1}+\mathrm{f}_{2}$
Median $\displaystyle =32.5 \therefore$ Median class is $\displaystyle 30-40$
$\displaystyle 32.5=30+\frac{20-\left(12+\mathrm{f}_{1}\right)}{12} \times 10$
$\displaystyle \Rightarrow \mathrm{f}_{1}=5$
$\displaystyle \because 32+\mathrm{f}_{1}+\mathrm{f}_{2}=40$
$\displaystyle \therefore \mathrm{f}_{2}=3$
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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.