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If the median of the distribution is given below is 28.5, find the values of x and y - CBSE Class 10 - Mathematics

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Question

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 Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 14: Statistics
Ex. 14.30 | Q: 2 | Page no. 287
Solution If the median of the distribution is given below is 28.5, find the values of x and y Concept: Median of Grouped Data.
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