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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. Find the missing frequencies x and y

Runs scored 2500 – 3500 3500 – 4500 4500 – 5500 5500 – 6500 6500 – 7500 7500 - 8500
Number of batsman 5 x y 12 6 2

1 Answer

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Best answer

We prepare the cumulative frequency table, as shown below:

Let x and y be the missing frequencies of class intervals 3500 – 4500 respectively. 

Then, 25 + x + y = 60 ⇒ x + y = 35 ……(1) 

Median is 5000, which lies in 4500 – 5500. So, the median class is 4500 – 5500. 

∴ l = 4500, h = 1000, N = 60, f = y and c f = 5 + x 

Now,

⇒ y = 50 – 2x

⇒ 35 – x = 50 – 2x [From (1)]

⇒ 2x – x = 50 – 35

⇒ x = 15

∴ y = 35 – x [From (1)]

⇒ y = 35 – 15

⇒ y = 20

Hence, x = 15 and y = 20.

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