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In the following data the median of the runs scored by 60 top batsmen of the world in one-day international cricket matches is 5000.

Runs scored
Frequency
2500-3500
5
3500-4500
X
4500-5500
Y
5500-6500
12
6500-7500
6
7500-8500
2

The missing frequencies x and y are and , respectively.

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Detailed Solution

The missing frequencies x and y are 15 and 20, respectively.
Given:

We know that the formula of median is

Median = l + h × N 2 − c f f

where,

l

=lower limit of the median class,

h

=size of the median class,

f

= frequency of the median class,

N

= sum of frequencies and

c f

=cumulative frequency of the class just preceding the median class.
The cumulative frequency distribution table will be:

25 + x + y = 60 x + y = 35...... 1

Calculating median:

Median = l + h × N 2 − c f f

5000 = 4500 + 1000 × 602 − 5 + x y

500 = 1000 × 30 − 5 − x y

y = 50 − 2 x ....... 2

Solve equations 1 and 2, we get

x = 15, y = 20

.
Thus, the missing frequencies x and y are 15,20.

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