Question

The mode of the following distribution is 65.625 hours. Find the value of p.
Lifetime (in hours) 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 10 35 52 60 p 29

Answer 1

Given :  

Lifetime (in hours) 0-20 20-40 40-60 60-80 80-100 100-120

Frequency             10       35         52       60        p         29

Mode  65.625

To Find : value of p

Solution:

Mode is  65.625  lies between   60-80

Lifetime (in hours)  f

0-20                    10

20-40                   35

40-60                   52

60-80                   60

80-100                  p

100-120                 29

Mode  =   60  +  20 * ( 60  - 52)/ (60 - 52 + 60 - p)

=> 65.625 = 60  +  20 * ( 8)/ ( 68 - p)

=> 5.625  = 160 / ( 68 - p)

=> p = 39.56

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