Question

The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.

Class	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40
Frequency	12	a	12	15	b	6	6	4

Answer 1

Let a and b be the missing frequencies of class intervals 5 – 10 and 20 – 25 respectively. 

Then, 55 + a + b = 70

⇒ a +b =15 …..(1) 

Median is 16, which lies in 15 – 20. So, the median class is 15 – 20. 

∴ l = 15, h = 5, N = 70, f = 15 and c f = 24 + a 

Now,

⇒ 1 × 3 = 11 – a 

⇒ a = 11 – 3 

⇒ a = 8 

∴ b = 15 – a [From (1)] 

⇒ b = 15 – 8 

⇒ b = 7 

Hence, a = 8 and b = 7.