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Lifetime (in hours) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
Frequency | 10 | 35 | 52 | 61 | 38 | 29 |
Answer :
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.