If the median of the distribution given below is 28.5, find the values of x and y
Solution:
Median class is the class having Cumulative frequency (cf) just greater than n/2
Median = l + [(n/2 - cf) / f] × h
Class size, h
Number of observations, n
Lower limit of median class, l
Frequency of median class, f
Cumulative frequency of class preceding median class, cf
The cumulative frequency for the given data is calculated as follows
From the table, it can be observed that n = 60 ⇒ n/2 = 30
45 + x + y = 60
x + y = 15 .....(i)
The median of the data is given as 28.5 which lies in interval 20 − 30.
Therefore, median class = 20 - 30
Class size, h = 10
Lower limit of median class, l = 20
Frequency of median class, f = 20
Cumulative frequency of class preceding the median class, cf = 5 + x
Median = l + [(n/2 - cf)/f] × h
28.5 = 20 + [(60/2 - (5 + x))/20] × 10
8.5 = (25 - x)/2
25 - x = 8.5 × 2
x = 25 - 17
x = 8
Putting x = 8 in equation (i)
8 + y = 15
y = 7
Hence, the values of x and y are 8 and 7 respectively.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 14
Video Solution:
If the median of the distribution given below is 28.5, find the values of x and y.
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 Question 2
Summary:
The values of x and y if the median of the distribution is 28.5 are 8 and 7 respectively.
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