The following data gives information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components.

Step 1: Recall the mode formula for the grouped data
Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h
l - The lower boundary of the modal class,
h - The class size,
f_1 - The frequency of modal class,
f_0 - the frequency of the class preceding the modal class,
f_2 the frequency of the class succeeding the modal class.
Step 2: Identify the modal class and locate the values of the frequencies.
NOTE: Locate a class with the maximum frequency, called the modal class.
(The mode is a value inside the modal class)
Here the maximum class frequency is 61, and the class corresponding to this
frequency is 60 - 80,
So, the modal class is 60 - 80.
lower boundary l = 60
Class size h = 80 - 60 = 20
The frequency of modal class f_1 = 61
The frequency of the class preceding the modal class f_0 = 52
The frequency of the class succeeding the modal class. f_2 = 38
Step 3: Substitute the values in the formula and calculate the mode.
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{9}{32} * 20
= 60 + \frac{9}{8} * 5
= 60 + 5.625
= 65.625
Hence, mode = 65.625