Question

An incomplete frequency distribution is given below

Variate	Frequency
10 – 20	12
20 – 30	30
30 – 40	?
40 – 50	65
50 – 60	45
60 – 70	25
70 – 80	18
Total	229

Median value is 46, the missing frequency is:

विकल्प

• 33.5

• 35

• 34

• 26

Answer 1

34

Explanation:

Median = 46 which lies in 40 – 50 class

Median = ${\displaystyle l+h\frac{\{\frac{n}{2}-C_f\}}{f}}$

where f = frequency of median-class

C_f cumulative frequency of the class preceding the median class.

∴ 46 = ${\displaystyle 40+10\frac{[\frac{229}{2}-(x+42)]}{65}}$

where x = frequency of class 30 – 40

${\displaystyle \Rightarrow }$ x = 33.5 = 34.