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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 4 · Set 1 · Q13
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…
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 | $\displaystyle 8$ | $\displaystyle 10$ | $\displaystyle 15$ | $\displaystyle 25$ | $\displaystyle 40$ | $\displaystyle 24$ | $\displaystyle 18$ |
(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 $\displaystyle 58$ . Find the value of $\displaystyle x$. Case Study - $\displaystyle 2$
Marking-scheme solution
\begin{table}
\captionsetup{labelformat=empty}
\caption{(a)}
\end{table}
$\displaystyle N=140, \therefore \frac{N}{2}=70$, which corresponds to $\displaystyle 55$-$\displaystyle 65$
∴ Median class = $\displaystyle 55$-$\displaystyle 65$\[\begin{array}{l}
\therefore l=55, f=40, c f=58, h=10 \\
\text { Median }=l+\frac{\dfrac{N}{2}-c f}{f} \times h \\
\quad=55+\frac{70-58}{40} \times 10=55+3=58 \\
\therefore \text { Median }=58
\end{array}
\]
| Age Group | No. of people (f) | Cf |
| $\displaystyle 15$-$\displaystyle 25$ | $\displaystyle 8$ | $\displaystyle 8$ |
| $\displaystyle 25$-$\displaystyle 35$ | $\displaystyle 10$ | $\displaystyle 18$ |
| $\displaystyle 35$-$\displaystyle 45$ | $\displaystyle 15$ | $\displaystyle 33$ |
| $\displaystyle 45$-$\displaystyle 55$ | $\displaystyle 25$ | $\displaystyle 58$ |
| $\displaystyle 55$-$\displaystyle 65$ | $\displaystyle 40$ | $\displaystyle 98$ |
| $\displaystyle 65$-$\displaystyle 75$ | $\displaystyle 24$ | $\displaystyle 122$ |
| $\displaystyle 75$-$\displaystyle 85$ | $\displaystyle 18$ | $\displaystyle 140$ |
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