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.