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	38	29

Determine the modal lifetimes of the components.

Answer 1

From the data given above, it can be observed that the maximum class frequency is 61, belonging to class interval 60 − 80.

Therefore, modal class = 60 − 80

Lower class limit (l) of modal class = 60

Frequency (f₁) of modal class = 61

Frequency (f₀) of class preceding the modal class = 52

Frequency (f₂) of class succeeding the modal class = 38

Class size (h) = 20

`"Mode" = l+((f_1-f_0)/(2f_1-f_0-f_2))xh`

=`60+((61-52)/(2(61)-52-38))(20)`

=`60+(9/(122-90))(20)`

=60+90/16=  60+5.625

= 65.625

Therefore, modal lifetime of electrical components is 65.625 hours.