# If the median of the distribution is given below is 28.5, find the values of x and y - Mathematics

If the median of the distribution is given below is 28.5, find the values of x and y

 Class interval Frequency 0 - 10 5 10 - 20 x 20 - 30 20 30 - 40 15 40 - 50 y 50 - 60 5 Total 60

#### Solution

The cumulative frequency for the given data is calculated as follows

 Class interval Frequency Cumulative frequency 0 - 10 5 5 10 - 20 x 5+ x 20 - 30 20 25 + x 30 - 40 15 40 + x 40 - 50 y 40+ x + y 50 - 60 5 45 + x + y Total (n) 60

From the table, it can be observed that n = 60
45 + x + y = 60
x + y = 15 (1)
Median of the data is given as 28.5 which lies in interval 20 - 30.

Therefore, median class = 20 - 30

Lower limit (l) of median class = 20

Cumulative frequency (cf) of class preceding the median class = 5 + x

Frequency (f) of median class = 20
Class size (h) = 10

"Median" = l + (((n/2)-cf)/f)xxh

28.5 = 20 + [(60/2-(5+x))/20]xx10

8.5 = ((25-x)/2)

17 = 25 - x

8 + y =  15

y = 7
Hence, the values of x and y are 8 and 7 respectively.

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#### APPEARS IN

NCERT Class 10 Maths
Chapter 14 Statistics
Exercise 14.3 | Q 2 | Page 287
RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.4 | Q 12 | Page 35