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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 5 · Set 1 · Q34
The mean of the following frequency distribution is 28. If sum of all frequencies is $\displaystyle 100$, then find the values of p and q : Class Interval $\displaystyle 0$-$\displaystyle 10$ $\displaystyle 10$-$\displaystyle 20$ $\displaystyle 20$-$\displaystyle 30$ $\displaystyle 30$-$\displaystyle 40$ $\displaystyle 40$-$\displaystyle 50$ $\displaystyle 50$-$\displaystyle 60$ Frequency $\displaystyle 12$ p $\displaystyle 27$ $\displaystyle 20$ q $\displaystyle 6$
Find median and mode of the following distribution : Class Interval $\displaystyle 0$-$\displaystyle 15$ $\displaystyle 15$-$\displaystyle 30$ $\displaystyle 30$-$\displaystyle 45$ $\displaystyle 45$-$\displaystyle 60$ $\displaystyle 60$-$\displaystyle 75$ $\displaystyle 75$-$\displaystyle 90$ $\displaystyle 90$-$\displaystyle 105$ Frequency $\displaystyle 15$ $\displaystyle 10$ $\displaystyle 12$ $\displaystyle 9$ $\displaystyle 8$ $\displaystyle 10$ $\displaystyle 6$
The mean of the following frequency distribution is 28. If sum of all frequencies is $\displaystyle 100$, then find the values of p and q :
| Class Interval | $\displaystyle 0$-$\displaystyle 10$ | $\displaystyle 10$-$\displaystyle 20$ | $\displaystyle 20$-$\displaystyle 30$ | $\displaystyle 30$-$\displaystyle 40$ | $\displaystyle 40$-$\displaystyle 50$ | $\displaystyle 50$-$\displaystyle 60$ |
| Frequency | $\displaystyle 12$ | p | $\displaystyle 27$ | $\displaystyle 20$ | q | $\displaystyle 6$ |
Find median and mode of the following distribution :
| Class Interval | $\displaystyle 0$-$\displaystyle 15$ | $\displaystyle 15$-$\displaystyle 30$ | $\displaystyle 30$-$\displaystyle 45$ | $\displaystyle 45$-$\displaystyle 60$ | $\displaystyle 60$-$\displaystyle 75$ | $\displaystyle 75$-$\displaystyle 90$ | $\displaystyle 90$-$\displaystyle 105$ |
| Frequency | $\displaystyle 15$ | $\displaystyle 10$ | $\displaystyle 12$ | $\displaystyle 9$ | $\displaystyle 8$ | $\displaystyle 10$ | $\displaystyle 6$ |
Marking-scheme solution
Class Interval
$\displaystyle 0$-$\displaystyle 10$
$\displaystyle 10$-$\displaystyle 20$
$\displaystyle 15$
$\displaystyle 27$
$\displaystyle 675$
$\displaystyle 700$
$\displaystyle 40$-$\displaystyle 50$
$\displaystyle 50$-$\displaystyle 60$
$\displaystyle 55$
\(\displaystyle 65+\mathrm{p}+\mathrm{q}\)
\(\displaystyle 15 p+45 q+1765\)
Z
\(\displaystyle \mathrm{f}_{\mathrm{i}}=100=65+\mathrm{p}+\mathrm{q} \Rightarrow \mathrm{p}+\mathrm{q}=35\)
Mean \(\displaystyle =28=\frac{15 \mathrm{p}+45 \mathrm{q}+1765}{100}\)
\(\displaystyle \Rightarrow \mathrm{p}+3 \mathrm{q}=69\)
On solving, we get \(\displaystyle \mathrm{p}=18, \mathrm{q}=17\)
\(\displaystyle \frac{70}{2}=35\), Median class is \(\displaystyle 30-45\)
Median \(\displaystyle =30+\frac{35-25}{12} \times 15\)
\[=\frac{85}{2}=42.5
\]
Modal class is \(\displaystyle 0-15\)
\[\begin{aligned}
\text { Mode } & =0+\frac{15-0}{30-0-10} \times 15 \\
& =\frac{45}{4}=11.25
\end{aligned}
\]
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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.