Question

The population of lions was noted in different regions across the world in the following table:

Number of lions	Number of regions
0 − 100	2
100 − 200	5
200 − 300	9
300 − 400	12
400 − 500	x
500 − 600	20
600 − 700	15
700 − 800	9
800 − 900	y
900 − 1000	2
	100

If the median of the given data is 525, find the values of x and y.

Answer 1

Median = 525

Number of lions	x	f	c.f.
0 − 100	50	2	2
100 − 200	150	5	7
200 − 300	250	9	16
300 − 400	350	12	28
400 − 500	450	x	28 + x
500 − 600	550	20	48 + x
600 − 700	650	15	63 + x
700 − 800	750	9	72 + x
800 − 900	850	y	72 + x + y
900 − 1000	950	2	74 + x + y
		`bb(sumf = 100)`

n = 100, `n/2 = 100/2` = 50

Median class = 500 − 600

l = 500, c.f. = 28 + x

h = 100, f₁ = 20

Then, 100 = 74 + x + y

100 − 74 = x + y

26 = x + y   ....(i)

Median = `l + ((n/2 - (f_0)))/(f_1) xx h`

525 = `500 + ([50 - (28 + x)])/20 xx 100`

525 – 500 = (50 − 28 − x)5

25 = (22 − x)5

`25/5` = 22 − x

5 = 22 − x

x = 22 − 5

x = 17

By equation (i),

26 = x + y

26 = 17 + y

26 − 17 = y

y = 9