Question

The weights (in kg) of 45 students of a class are given

in the following distribution table. Determine the

value of weight x which is such that the number of

students having weight less than x kg is same as the

number of students having weight more than x kg.

Answer 1

Given : The weights (in kg) of 45 students of a class

To find :  the  value of weight x which is such that the number of   students having weight less than x kg is same as the   number of students having weight more than x kg.

Solution:

We need to find Median Here:

Below 45       5           5               - 45

Below 50      11            6           45 - 50  

Below 55      15           4           50 - 55  

Below 60      22          7           55 - 60  

Below 65      38          16          60 - 65  

Below 70      45           7          65 - 70  

Total Students = 45

23 rd student is median Student

Which lies in  22 - 38  

Median =  60 +  5 x  (45/2 - 22) /16

= 60 +  5 x 0.5/16

= 60 + 0.15625

= 60.16  kg

60.16  kg is the Weight such that number of  students having weight less than 60.16 kg is same as the  number of students having weight more than 60.16 kg.

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