Question 28 (Or 1st) - CBSE Class 10 Sample Paper for 2019 Boards - Solutions of Sample Papers for Class 10 Boards
Last updated at April 16, 2024 by Teachoo
Question 28 (OR 1
st
question)
The median of the following data is 525. Find the values of x and y if the total frequency is 100.
Class Interval
Frequency
0 – 100
2
100 – 200
5
200 – 300
x
300 – 400
12
400 – 500
17
500 – 600
20
600 – 700
y
700 – 800
9
800 – 900
7
900 – 100
4
Transcript
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 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, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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