Question

The median of the following frequency distribution is 25. Find the value of x.

Class:	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency:	6	9	10	8	x

Answer 1

Class Interval	Frequency	Cumulative frequency (`C_f`)
0 – 10	6	6
10 – 20	9	15
20 – 30	10	25
30 – 40	8	33
40 – 50	x	33 + x
	`sumf_i` = 33 + x

Total frequency = 33 + x

i.e., N = 33 + x

∴ `"N"/2 = (33 + x)/2`

Median = 25

So class corresponding to this 20 – 30,

So, l = 20, `"C"_f` = 15, `f` = 10 and h = 10

Median = `"l" + ((N/2 - c_f)/f) xx "h"`

⇒ 25 = `20 + (((33  +  x)/2 - 15)/10) xx 10`

⇒ 25 = `20 + (33 + x - 30)/2`  ...[Given, Median = 25]

⇒ 25 – 20 = `(3 + x)/2`

⇒ 10 = 3 + x

⇒ x = 7