# 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. Given: Median = 5000 & N = 60

Assume

Σfi = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and Cf = cumulative frequency

Lets form a table, where x is the unknown frequency. Given,
Median = 5000 (as already mentioned in the question)

Sum of frequencies, N = x + y + 25 = 60 [Total No of players]

5000 lies between 4500 - 5500 Median class = 4500 - 5500

l = 4500, h = 1000, f = y, N/2 = 60/2=30
and Cf = 5 + x

Median is given by,   5000 – 4500 = (25000 – 1000x)/y

500y = 25000 – 1000x

2x + y = 50 …(i)

And given that N = 60

25 + x + y = 60

x + y = 35 …(ii)

Solving equations (i) & (ii), we get

(2x + y) – (x + y) = 50 – 35

x = 15

Substituting x = 15 in eq.(ii),

15 + y = 35

y = 20

Thus, the unknown frequencies are x = 15 and y = 20.

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