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# 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.