The median of the following data is 525


Asked by admin @ in Math viewed by 346 People


The median of the following data is 525. Find the value of x and y, if the sum of frequency is 100:

Class
0-100
100-200
200-300
300-400
400-500
500-600
600-700
700-800
800-900
900-1000
Frequency
3
4
x
12
17
20
9
y
8
3

Answered by admin @



HELLO DEAR,

MEDIAN IS 525
500 - 600 is median class


we know median = \bold{ l + \frac{\frac{n}{2} - cf}{f} * h}


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 = \bold{ 500 + \frac{\frac{100}{2} - (36 + x)}{20} * 100}

⇒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


I HOPE ITS HELP YOU DEAR,
THANKS






















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