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Q.

The maximum bowling speeds, in km per hour, of $33$ players at a cricket coaching center are given as follows.

The median bowling speed in km/hr is

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a

109.17 km/hr

b

110 km/hr

c

115 km/hr

d

118.2 km/hr

answer is A.

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Detailed Solution

It is given that, a table of data.
Question Image

Question Image

Obtain the cumulative frequency of all the classes and the number of observations

N

.
Cumulative frequency of each class is found by adding frequency with the succeeding frequencies.
For the class 85 - 100, the frequency is 11.
The cumulative frequency is 11.
For the class 100 - 115, the frequency is 9.
The cumulative frequency is 11 + 9 = 20.
For the class 115 - 130, the frequency is 8.
The cumulative frequency is 20 + 8 = 28.
For the class 130 - 145, the frequency is 5.
The cumulative frequency is 28 + 5 =33.
By constructing the cumulative frequency, we get,
Question Image

Question Image

Obtain the class from the table, whose cumulative frequency is greater than and nearest to

N 2

.
The sum of the frequency is

N 2 = 332

= 16.5

The corresponding class will be

100 − 115

.
So, median lies in this group, and the lower limit for this interval is

100

, cumulative frequency is

11

, and frequency is 9.
The median of the data is,

= l + (N 2 − c f f) × h

Where

l

is the lower limit of the median class,

h

is the class size and

c f

will be the cumulative frequency of class interval preceding the median class.
By substituting the known values within the above formula,’

= 100 + (16.5 − 11 9) × 15

= 100 + 9.17

= 109.17

km/hr
The required value is

109.17 k m / h o u r

.
Hence, option 1 is correct.

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