The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.
Salary(in thousands)No. of people5−10710−151215−201520−25825−301130−351835−4010
₹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