The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetime (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.

The class 60-80 has the maximum frequency, therefore, this is the modal class.

Here l = 60 , h = 20 , f₁ = 61 , f₀ = 52 , and f₂ = 38

Now, let us substitute these values in the formula

\(Mode \ = \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)

\( = \ 60 \ + \ ( \frac{61 \ - \ 52}{2 \ × \ 61 \ - \ 52 \ - \ 38}) \ × \ 20 \)

\(= \ 60 \ + \ ( \frac{61 \ - \ 52}{122 \ - \ 52 \ - \ 38}) \ × \ 20 \)

\(= \ 60 \ + \ \frac{9}{32} \ × \ 20 \)

\( = \ 60 \ + \ 5.625 \ = \ 65.625 \)

\(\therefore \) The modal lifetimes of the components is 65.625 hours.