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 21st of June every year since 2015.
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 :
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding stimulus
Model Answer
(a) Median Age:
| Age Group | Frequency | Cumulative Frequency |
|-----------|-----------|----------------------|
| 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 |
Total N = 140, so N/2 = 70.
Median class = 55–65 (cf = 58, f = 40, l = 55, h = 10)
$$\text{Median} = 55 + \frac{70 - 58}{40} \times 10 = 55 + 3 = \mathbf{58}$$
(b) Finding x:
Original Σfi·xi (midpoints: 20, 30, 40, 50, 60, 70, 80):
Σfi·xi = 8(20)+10(30)+15(40)+25(50)+40(60)+24(70)+18(80)
= 160+300+600+1250+2400+1680+1440 = 7830
New total frequency = 140 + x; New Σfi·xi = 7830 + 70x
$$58 = \frac{7830 + 70x}{140 + x}$$
$$8120 + 58x = 7830 + 70x \implies 290 = 12x \implies \boxed{x = \frac{290}{12} \approx 24.17}$$
Since x must be a whole number, x ≈ 24 (or exact value $x = \dfrac{145}{6}$, accept as per calculation).
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Explanation
- Part (a): Always build cumulative frequency, identify median class where cf first exceeds N/2, then apply the formula correctly. Here median = 58.
- Part (b): Use midpoints for mean calculation. Set up the equation with (140 + x) in denominator and solve. If the answer is non-integer, present the exact fraction — CBSE accepts it. Show all steps clearly for full marks.