CBSE 2025 · Region 2 · Set 1 · Q35 · 5 marks

Find the Mean and Mode of the following frequency distribution :
Class Frequency
$\displaystyle 0$-$\displaystyle 10$ $\displaystyle 8$
$\displaystyle 10$-$\displaystyle 20$ $\displaystyle 7$
$\displaystyle 20$-$\displaystyle 30$ $\displaystyle 15$
$\displaystyle 30$-$\displaystyle 40$ $\displaystyle 20$
$\displaystyle 40$-$\displaystyle 50$ $\displaystyle 12$
$\displaystyle 50$-$\displaystyle 60$ $\displaystyle 8$
$\displaystyle 60$-$\displaystyle 70$ $\displaystyle 10$

StatisticsMean of Grouped DataApplylong_answermedium

Class	frequency \(\displaystyle \left(f_{\mathrm{i}}\right)\)	\(\displaystyle x_{\mathrm{i}}\)	\(\displaystyle u_{\mathrm{i}=\frac{x_{i}-35}{10}}\)	\(\displaystyle f_{\mathrm{i}} u_{\mathrm{i}}\)
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 8$	$\displaystyle 5$	-$\displaystyle 3$	-$\displaystyle 24$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle 7$	$\displaystyle 15$	-$\displaystyle 2$	-$\displaystyle 14$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 15$	$\displaystyle 25$	-$\displaystyle 1$	-$\displaystyle 15$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 20$	\(\displaystyle 35=\mathrm{a}\)	$\displaystyle 0$	$\displaystyle 0$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle 12$	$\displaystyle 45$	$\displaystyle 1$	$\displaystyle 12$
$\displaystyle 50$-$\displaystyle 60$	$\displaystyle 8$	$\displaystyle 55$	$\displaystyle 2$	$\displaystyle 16$
$\displaystyle 60$-$\displaystyle 70$	$\displaystyle 10$	$\displaystyle 65$	$\displaystyle 3$	$\displaystyle 30$
Total	$\displaystyle 80$			$\displaystyle 5$

Marking-scheme solution