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.

Answer 1

Here , frequency of class interval $60-80$ is maximum.
So, it is the modal class
Now, $l=$ Lower limit of modal class $=60$
$f_1=$ Frequency of modal class $=61$
$f_0=$ Frequency of class preceding the modal class $=52$
$f_2=$ Frequency of class succeeding the modal class $=38$
$h=$ Class interval width = 20

So, Mode $=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$

$=60+\left(\frac{61-52}{2\left(61\right)-52-38}\right)\times 20$

$=60+\left(\frac{9}{122-90}\right)\times 20$

$=60+\left(\frac{9}{32}\right)\times 20$

$=60+5.625$

Mode $=65.625$
Therefore, modal lifetime of electrical components is $65.625$ hours