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

Medical check-up was carried out for $\displaystyle 35$ students of a class and their weights were recorded as follows :
Weight (in kg) $\displaystyle 38$-$\displaystyle 40$ $\displaystyle 40$-$\displaystyle 42$ $\displaystyle 42$-$\displaystyle 44$ $\displaystyle 44$-$\displaystyle 46$ $\displaystyle 46$-$\displaystyle 48$ $\displaystyle 48$-$\displaystyle 50$ $\displaystyle 50$-$\displaystyle 52$
Number of Students $\displaystyle 3$ $\displaystyle 2$ $\displaystyle 4$ $\displaystyle 5$ $\displaystyle 14$ $\displaystyle 4$ $\displaystyle 3$
Find the difference between the mean weight and the median weight.

StatisticsMean of Grouped DataApplylong_answermedium

Weight (in kg)	Number of Students ( \(\displaystyle f_{\mathrm{i}}\) )	\(\displaystyle x_{\mathrm{i}}\)	\(\displaystyle u_{\mathrm{i}=\frac{x_{i}-45}{2}}\)	\(\displaystyle f_{\mathrm{i}} u_{\mathrm{i}}\)	\(\displaystyle c f\)
$\displaystyle 38$-$\displaystyle 40$	$\displaystyle 3$	$\displaystyle 39$	-$\displaystyle 3$	-$\displaystyle 9$	$\displaystyle 3$
$\displaystyle 40$-$\displaystyle 42$	$\displaystyle 2$	$\displaystyle 41$	-$\displaystyle 2$	-$\displaystyle 4$	$\displaystyle 5$
$\displaystyle 42$-$\displaystyle 44$	$\displaystyle 4$	$\displaystyle 43$	-$\displaystyle 1$	-$\displaystyle 4$	$\displaystyle 9$
$\displaystyle 44$-$\displaystyle 46$	$\displaystyle 5$	\(\displaystyle 45=\mathrm{a}\)	$\displaystyle 0$	$\displaystyle 0$	$\displaystyle 14$
$\displaystyle 46$-$\displaystyle 48$	$\displaystyle 14$	$\displaystyle 47$	$\displaystyle 1$	$\displaystyle 14$	$\displaystyle 28$
$\displaystyle 48$-$\displaystyle 50$	$\displaystyle 4$	$\displaystyle 49$	$\displaystyle 2$	$\displaystyle 8$	$\displaystyle 32$
$\displaystyle 50$-$\displaystyle 52$	$\displaystyle 3$	$\displaystyle 51$	$\displaystyle 3$	$\displaystyle 9$	$\displaystyle 35$
Total	$\displaystyle 35$			$\displaystyle 14$

Marking-scheme solution