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 the 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))xxh`

= `60+((61-52)/(2(61)-52-38))xx20`

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

= `60+90/16`

= 60 + 5.625

= 65.625

Therefore, the modal lifetime of electrical components is 65.625 hours.