Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age (in years)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Number of persons	5	25	?	18	7

Answer 1

Let the missing frequency be x.
To find the median let us put data in the table given below:

Age (in years)	Number of persons (f)	Cumulative frequency (cf)
0 – 10	5	5
10 – 20	25	30
20 – 30	x	30 + x
30 – 40	18	48 + x
40 – 50	7	55 + x

The given median is 24,
∴ The median class is 20 – 30.

∴ l = 20, ℎ = 10, 𝑁 = 55 + 𝑥, 𝑓 = 𝑥 𝑎𝑛𝑑 𝑐𝑓 = 30

𝑀𝑒𝑑𝑖𝑎𝑛 = 𝑙 +`((N/2 -cf)/f) xx h`

⇒ 24 = 20 + `(((55+x)/2-30)/x) xx 10`

⇒ `24-20 = ((55+x-60)/(2x))xx 10`

`⇒ 4= ((x-5)/(2x)) xx 10`

⟹ 8𝑥 = 10𝑥 − 50
⟹ 2𝑥 = 50
⟹ 𝑥 = 25
Thus, the missing frequency is 25.