# The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:Lifetimes (in hours):0-2020-4040-6060-8080-100100-120No. of components:103552613829Determine the modal lifetimes of the components."

Given:

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

To do:

We have to determine the modal lifetimes of the components.

Solution:

The frequency of the given data is as given below.

 Lifetimes (in hours) ($x_i$): No. of components $(f_i$): 0-20 10 20-40 35 40-60 52 60-80 61 80-100 38 100-120 29

We observe that the class interval of 60-80 has the maximum frequency(61).

Therefore, it is the modal class.

Here,

$l=60, h=20, f=61, f_1=52, f_2=38$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=60+\frac{61-52}{2 \times 61-52-38} \times 20$

$=60+\frac{9}{122-90} \times 20$

$=60+\frac{180}{32}$

$=60+5.625$

$=65.625$

The modal lifetimes of the components are 65.625 years.

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