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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 |
No. of components: | 10 | 35 | 52 | 61 | 38 | 29 |
Given:
The given data gives the 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 is 65.625 years.
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