Q. 24.4( 272 Votes )

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

Answer :

Let's make a cumulative frequency table for the above problem

Total frequency, N= 60

Now,

Given median = 28.5, lies in 20 - 30

Median class = 20-30

frequency corresponding to median class, f = 20

cumulative frequency of the class preceding the median class, cf = 5 + x

Lower limit, l = 20

class height, h = 10

Now,

Median can be calculated as:

28.5

28.5 - 20 =

8.5 =

25 –x =8.5 × 2

⇒ 25 - x = 17

⇒ x = 25-17

⇒ x = 8

Now,

From the cumulative frequency we can find the value of x + y as:

45 +x +y = 60

⇒ x + y = 60 - 45

⇒ x + y = 15

⇒ y = 15 – x

as, x = 8

⇒ y = 15 – 8

⇒y = 7

Hence,

Value of x = 8 and y = 7

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