Question

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

Class	0 – 10	10 – 20	20 – 30	30 – 40	40 - 50
Frequency	5	25	?	18	7

 

 

Answer 1

Class	Frequency (fi)	Cumulative Frequency (cf)
0 – 10	5	5
10 – 20	25	30
20 – 30	x	x+30
30 – 40	18	x+48
40 – 50	7	x+55

Median is 24 which lies in 20 – 30
∴ Median class = 20 – 30
Let the unknown frequency be x.

Here, l = 20, `n/2 = (x+55)/2`, c.f. of the preceding class = c.f = 30, f = x, h = 10
Now,
Median, `M = l + (n/2−cf)/f× h`
     `⇒ 24 = 20 + (x+55/2 − 30)/x × 10`
      `⇒ 24 = 20 + (x + 55 − 60/2)/ x × 10`
       ⇒ 24 = 20 +` (x−5 )/(2x) `× 10
       ⇒ 24 = 20 + `(5x−25)/ x`
       ⇒ 24 = 20+`( 5x−25)/ x`
       ⇒ 24x = 25x – 25
      ⇒ –x = – 25
     ⇒ x = 25
Hence, the unknown frequency is 25.