Question

The median of the following data is 52.5. find the value of x and y, if the total frequency is 100.


Class Interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90- 100


frequency 2 5 X 12 17 20 Y 9 7 4

Answer 1

x = 9 & y = 15

Step-by-step explanation:

Class         f                cf

0 - 10         2               2

10-20         5               7

20-30        x               7 + x

30-40        12              19 + x

40-50        17              36 + x

50-60        20             56 + x

60-70         y               56 + x + y

70-80         9               65 + x + y

80-90         7               72 + x + y

90-100        4              76 + x + y

76 + x + y = 100

=> x + y = 24

Median = 52.5

Median =  50   + 10 (  50  - (36 + x)/20

=> 52.5 = 50 + (14 - x)/2

=> 5 = 14 - x

=> x = 9

9 + y = 24

=> y = 15

x = 9 & y = 15

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