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
Made by
Davneet Singh
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo
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