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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.
Solution
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.
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