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Question

The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.

Salary(in thousands)No. of people510710151215201520258253011303518354010


A

₹27757.5

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B

₹21287.5

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C

₹24007.5

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D

₹24062.5

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Solution

The correct option is D

₹24062.5


The Cumulative frequency table is given as :

Salary(in thousands)Cumulative frequency<107<1519<2034<2542<3053<3571<4081

N = 81 (An odd number)

Median = (81+1)2th observation = 41st observation.

So, the Median class is 20000 - 25000.

We know that there are 8 people from the 34th to the 42nd person whose salary is between ₹20000 and ₹25000.

However, we do not know their individual salaries.

We will divide ₹5000 from ₹20000 to ₹25000 into 8 equal parts and assume that one person is in each subdivision.

We will assume that the salary of each person in a subdivision is the mid - value of the subdivision.

So, the salary of the 35th person is the mid value of ₹20000 and ₹2000050008, that is ₹20000500016

So, from the 35th person to the 41st person, there are 6 people.

If the 35th term of the AP is 20000500016 and the common difference is 50008,

Then the 41st term = 20000500016 + 6×50008

= 20000+5000+6000016

= 20000+6500016

= 20000 + 4062.5

= ₹24062.5


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