#### 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 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.

Is there an error in this question or solution?

Solution The following data gives the information on the observed lifetimes (in hours) of 225 electrical components Concept: Mode of Grouped Data.