Question

runs scored by 60 top bats,
et matches is 5000. Find
TUBSE 2013
9. In the following data the median of the runs score
of the world in one-day international cricket matches
missing frequencies x and y.
Runs scored 2500–3500/3500–4500 4500-5500 5500-6500 65
Number of
5 x | y |
batsmen
12
500-6500 6500–7500 7500-850​

Answer 1

x = 15 & y = 20

Step-by-step explanation:

Given that,

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

As we know,

N = ∑fi = 60

⇒ 35 + x + y = 60

From this, we know;

x + y = 60 - 25

∵ x + y = 35        ...(i)

Because the median = 5000 which lies in the class between 4500−5500

∵ l = 4500,

h = 1000(5500 - 4500)

f = y,

F = 5+x

N = 60

Median = l + (N/2 - F)/f * h

5000 = 4500 + (60/2 - y) * 1000

500y = 25 - x * 1000

y/2 = 25 - x

y = 50 − 2x

⇒2x + y = 50       ...(ii)

From equations (i) and (ii) we get

2x + (35 − x) = 50

x = 15

by putting x = 15 in equation (i),

we get y = 20(35-15)

Hence, x = 15 and y = 20

Learn more: find the cumulative frequency

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