CBSE 2022 · Region 4 · Set 2 · Q14

Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on $\displaystyle 21{ }^{\text {st }}$ of June every year since 2015. To promote Yoga, Green park society in Pune organised a $\displaystyle 7$-day Yoga camp in their society. The number of people of different age groups who enrolled for this camp is given as follows :

Age Group	$\displaystyle 15$-$\displaystyle 25$	$\displaystyle 25$-$\displaystyle 35$	$\displaystyle 35$-$\displaystyle 45$	$\displaystyle 45$-$\displaystyle 55$	$\displaystyle 55$-$\displaystyle 65$	$\displaystyle 65$-$\displaystyle 75$	$\displaystyle 75$-$\displaystyle 85$
Number of People	$\displaystyle 8$	$\displaystyle 10$	$\displaystyle 15$	$\displaystyle 25$	$\displaystyle 40$	$\displaystyle 24$	$\displaystyle 18$

Based on the above, find the following :

(a)

Find the median age of people enrolled for the camp.

(b)

If $\displaystyle x$ more people of age group $\displaystyle 65$-$\displaystyle 75$ had enrolled for the camp, the mean age would have been 58. Find the value of $\displaystyle x$.