Question

An incomplete distribution is given as follows:
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula fill up the missing frequency.
Variable: 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency: 10 20 ? 40 ? 25 15

Answer 1

The missing frequencies are 25 and 35

Step-by-step explanation:

Step 1 :

Given,

Median value = 35

Sum of all the frequency = 170

Step 2 :

Let x and y be the missing frequencies.

Sum of the given frequencies = 10 + 20 + x + 40 + y + 25 + 15 = 110 + x + y

So 110 + x + y = 170

 x + y = 60

Step 3 :

The formula for median is given by

Median = l + (n/2 -cf )h /f

where

median = 35 , so median class = 30-40

l = lower limit of the median class  = 30

n = sum of frequencies = 170/2 = 85

cf = cumulative frequency of the class before the median class = 30 + x

h = class interval =10

f = the median class 's frequency = 40

Substituting the above values,

30 + (85 - (30+x)) *10 divided by 40

=> 85 - 30 - x =>20

=> 55 - x = 20 => x = 35

Step 4:

From step 2 we have ,

x + y = 60 , x = 35

so y = 25

Step 5 :

The missing frequencies are 25 and 35

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