Question

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 the 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:

 

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:

1. Find the median age of people enrolled for the camp.
2. If x more people of the age group 65 – 75 had enrolled for the camp, the mean age would have been 58. Find the value of x.

Answer 1

a.

Age Group	No. of People (f)	c.f.
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
	`sum"f"` = 140

Here, N = `sum"f"` = 140

So, `"N"/2` = 70

Therefore, median class = 55 – 65

Lower limit of median class, l = 55

Cass size, h = 10

Cumulative frequency of preceding class, c.f. = 58

Frequency of median class, f = 40

∴ Median = `"l" + (("N"/2 - "c.f."))/"f" xx "h"`

= `55 + ((70 - 58)/40) xx 10`

= `55 + 12/4`

= 55 + 3

= 58

Thus, the median age of people enrolled for the camp is 58.

b. 

Age Group	Mid point (xi)	Frequency (fi)	fixi
15 – 25	20	8	160
25 – 35	30	10	300
35 – 45	40	15	600
45 – 55	50	25	1250
55 – 65	60	40	2400
65 – 75	70	24 + x	1680 + 70x
75 – 85	80	18	1440
		`sum"f"_"i"` = 140 + x	`sum"f"_"i""x"_"i"` = 7830 + 70x

Mean = `(sum"f"_"i""x"_"i")/(sum"f"_"i")`

⇒ 58 = `(7830 + 70"x")/(140 + "x")`

⇒ 58(140 + x) = 7830 + 70x

⇒ 8120 + 58x = 7830 + 70x

⇒ 12x = 290

⇒ x = 24.16 ∼ 24  ...(Approx)