Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not only make our body healthy but also achieve inner peace and calmness. The International Yoga Day is c

Question

Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not only make our body healthy but also achieve inner peace and calmness. The International Yoga Day is celebrated on $21^{st}$ of June every year since 2015.

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To promote Yoga, Green park society in Pune organised a 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 | $15$-$25$ | $25$-$35$ | $35$-$45$ | $45$-$55$ | $55$-$65$ | $65$-$75$ | $75$-$85$ |
|-----------|-----------|-----------|-----------|-----------|-----------|-----------|----------|
| Number of People | $8$ | $10$ | $15$ | $25$ | $40$ | $24$ | $18$ |

Based on the above, find the following:
(a) Find the median age of people enrolled for the camp.

Accepted Answer

Step 1: | Age Group | No. of people ($f$) | $cf$ |
|-----------|---------------------|------|
| $15$-$25$ | $8$ | $8$ |
| $25$-$35$ | $10$ | $18$ |
| $35$-$45$ | $15$ | $33$ |
| $45$-$55$ | $25$ | $58$ |
| $55$-$65$ | $40$ | $98$ |
| $65$-$75$ | $24$ | $122$ |
| $75$-$85$ | $18$ | $140$ |
Step 2: $N = 140$, $\frac{N}{2} = 70$, which corresponds to $55$-$65$
$	herefore$ Median class $= 55$-$65$
Step 3: $	herefore l = 55$, $f = 40$, $cf = 58$, $h = 10$
Median $= l + \frac{\frac{N}{2} - cf}{f} 	imes h$
$= 55 + \frac{70 - 58}{40} 	imes 10 = 55 + 3 = 58$
Step 4: $	herefore$ Median $= 58$

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