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

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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

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.