Question 28 (OR 1st question)
The median of the following data is 525. Find the values of x and y if the total frequency is 100.
Given that total frequency is 100
So,
Sum of frequency = 100
2 + 5 + x + 12 + 17 + 17 + 20 + y + 8 + 7 + 4 = 100
76 + x + y = 100
x + y = 100 – 76
x + y = 24
Now, to find values of x and y,
We first find median
Since Median is 525
500 – 600 is the median class
Median = l + (𝑛/2 − 𝑐𝑓)/𝑓 × h
Where
l = lower limit of median class
= 500
h = class-interval = 100 − 0 = 100
n = ∑▒𝑓𝑖 = 100
cf = cumulative frequency of the class before median class = 36 + x
f = frequency of the median class = 20
Now,
Median = l + (𝑛/2 −𝑐𝑓)/𝑓 × h
525 = 500 + (100/2 − (36 + 𝑥))/20 × 100
525 – 500 = (50 − (36 + 𝑥))/20 × 100
25 = (14 − 𝑥)/20 × 100
25 = (14 – x) × 5
25 = 70 – 5x
5x = 70 – 25
5x = 45
x = 45/9
x = 5
Now, from (1)
x + y = 24
Putting x = 5
5 + y = 24
y = 24 – 5
y = 19
Thus, x = 5, y = 19

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.