Question

Question 2
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:

$\begin{array}{ccccccc}\text{Lifetimes(in hours)}& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ \text{Frequency}& 10& 35& 52& 61& 38& 29\end{array}$

Determine the modal lifetimes of the components.

Answer 1

From the data given above, we observe that maximum class frequency is 61 of class interval 60 - 80.

So, modal class = 60 - 80

Lower class limit $l$ of modal class = 60

Frequency $\left(f_1\right)$ of modal class = 61

Frequency $\left(f_0\right)$ of class preceding the modal class = 52

Frequency $\left(f_2\right)$ of class succeeding the modal class = 38

Class size $h$ = 20

$\text{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h=60+\left(\frac{61-52}{2\left(61\right)-52-38}\right)\left(20\right)=60+\left(\frac{9}{122-90}\right)\left(20\right)=60+\left(\frac{9\times 20}{32}\right)=60+\frac{90}{16}=60+5.625=65.625$

So, modal lifetime of electrical components is 65.625 hours.