Question

Example 8 : 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
100 - 200
200-300
300 - 400
400 - 500
500 - 600
600 - 700
700 - 800
800 - 900
900 - 1000​

Answer 1

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MEDIAN IS 525

500 - 600 is median class

We know median = where, l = lower limit of median class = 500

h = class interval = 100 - 0 = 100

∑f_i = n = 100

cf = cumulative frequency before class median = 36 + x

f = median frequency

525 ⇒525 = 500 + {50 - (36 + x)} * 5

⇒525 - 500 = {50 - (36 + x)}*5

⇒25/5 = 50 - (36 + x)

⇒36 + x = 50 - 5

⇒x = 45 - 36

⇒x = 9

And

∑f_i = 76 + x + y

100 = 76 + x + y

9 + y + 76 = 100

y = 100 - 85

y = 15