Question

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

Lifetime (in hours)	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$
Frequency	$10$	$35$	$52$	$61$	$38$	$29$

Answer 1

According to the given parameters

The modal class is $60-80$; $l=60,$ and the frequencies are$f_m=61,f_1=52,f_2=38andh=20$

The formula to find the mode is

$Mode=l+\left[\frac{(f_m-f_1)}{(2f_m-f_1-f_2)}\right]\times h$

$$\begin{gathered} =60+\left[\frac{(61-52)}{(122-52-38)}\right]\times 20 \\ =60+\left(\frac{\left(\right(9x20)}{32}\right) \\ =60+\frac{45}{8} \\ =60+5.625 \\ =65.625hours. \end{gathered}$$

Hence, the modal lifetime of the components $65.625hours.$