Question

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

Answer 1

We prepare the cumulative frequency table, as shown:

Runs scored	No. of batsmen	Cumulative frequency
2500-3500	5	5
3500-4500	x	5+x
4500-5500	y	5+x+y
5500-6500	12	17+x+y
6500-7500	6	23+x+y
7500-8500	2	25+x+y
Total	N=Σfi=60

Let x,y be the missing frequencies of class intervals 3500-4500 and 4500-5500 respectively.

Then,

25 + x + y = 60

⇒x+y=35 ----------(i)

Median is 5000, which lies in 4500-5500.

So the median class is 4500-5500.

Therefore, l= 4500, h= 1000, N= 60, f= y, and cf = 5+x

Now,

Median,M=l+((N/2−cf) /f)×h

⇒5000–4500 = ((30–5–x)/y)×1000

⇒500 = ((25−x)/y)×1000

⇒y = 50–2x

⇒35–x=50–2x ( From (i) )

⇒2x–x=50–35

⇒x=15

Therefore, y=35–x

⇒y=35–15

⇒y=20

Hence, x= 15 and y = 20.