Question

The given distribution shows the number of runs scored by some top batsmen of the world in one day international cricket matches.
Runs scored No of batsmen Runs scored No of batsmen
3000 – 4000 4 7000 – 8000 6
4000 – 5000 18 8000 – 9000 3
5000 – 6000 9 9000 – 10000 1
6000 – 7000 7 10000 – 11000 1
Find the mode of the data.

Answer 1

SOLUTION :  

FREQUENCY DISTRIBUTION TABLE is in the attachment

For MODE :

Here the maximum frequency is 18, and the class corresponding to this frequency is 4000 – 5000. So the modal class is 4000 – 5000.

Therefore, l = 4000, h = 100,  f1= 18,  f0= 4 , f2 = 9

Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h

= 4000 + [(18 - 4)/(2 × 18 - 4 – 9) ] ×1000

= 4000 + [14 × 1000)/(36 - 13)]

= 4000 + [14000/ 23]

= 4000 + 608.7

= 4608.7

MODE = 4608.7

Hence, the mode of the data is 4608.7.

★★ Mode = l + (f1-f0/2f1-f0-f2) ×h

l = lower limit of the modal class

h = size of the class intervals

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeed in the modal class.

HOPE THIS ANSWER WILL HELP YOU…