Question

The following data gives the information on the observed lifetimes in hours) of 225
electrical components:
Lifetimes (in hours)
0-20
20-40
40-60
60-80
80 - 100
100-120
Frequency
10
35
52
61
Determine the modal lifetimes of the components.
​

Answer 1

Step-by-step explanation:

Here , frequency of class interval 60−80 is maximum.

So, it is the modal class

Now, l= Lower limit of modal class =60

f

1

= Frequency of modal class =61

f

0

= Frequency of class preceding the modal class =52

f

2

= Frequency of class succeeding the modal class =38

h= Class interval width = 20

So, Mode =l+(

2f

1

−f

0

−f

2

f

1

−f

0

)×h

=60+(

2(61)−52−38

61−52

)×20

=60+(

122−90

9

)×20

=60+(

32

9

)×20

=60+5.625

Mode =65.625

Therefore, modal lifetime of electrical components is 65.625 hours