Question

[CBSE 2013]
9. 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
12
I 2
batsmen​

Answer 1

Answer:

Step-by-step explanation:

Given 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

12

I 2

batsmen

Given

Runs scored             Number 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

Now N = ∑ fi = 60

25 + x + y = 60

So x + y = 35----------1

According to question median is 5000 and it lies in 4500 – 5500

So l = 4500, h = 1000, f = y, F= 5 + x, N = 60

Now median = l + N/2 – F / f x h

         5000 = 4500 + 60/2 – (5 + x) / y x 1000

5000 – 4500 = 30 – 5 – x / y  x 1000

500 / 1000 = 25 – x

Y = 50 – 2 x

2 x + y = 50 -----------2

From 1 and 2 we get

2 x + (35 – x) = 50

x = 15

2(15) + y = 50

y = 20

Answer 2

here is your answer

X=15 and Y=15