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.

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#### Solution

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 class 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+((f_1-f_0)/(2f_1-f_0-f_2))xh`

=`60+((61-52)/(2(61)-52-38))(20)`

=`60+(9/(122-90))(20)`

=60+90/16= 60+5.625

= 65.625

Therefore, modal lifetime of electrical components is 65.625 hours.

Concept: Mode of Grouped Data

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