# 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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