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	28	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 limit ($l$) of modal class = 60
Frequency ($f_1$) of modal class = 61
Frequency ($f_0$) of class preceding the modal class = 52
Frequency ($f_2$) of class succeeding the modal class = 38
Class size ($h$) = 20

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

Mode = 60$+ (\frac{61 - 52 }{ 2(61) - 52 - 38}) \times(20)$

Mode =$60+ [\frac{9}{122 - 90}] \times 20$

Mode = $60 +( \frac{9 \times20}{ 32})$
Mode = $60 + \frac{90}{16}$
Mode = 60 + 5.625
Mode = 65.625

Therefore, modal lifetime of electrical components is 65.625 hours.