Question

The following data shows the warranty period of different components. Find the modal warranty period.

$$\begin{array}{ccccccc}\text{Warranty period (years)}& 0-1& 1-2& 2-3& 3-4& 4-5& 5-6\\ \text{Number components}& 6& 10& 16& 25& 16& 20\end{array}$$

• A. 3
• B. 3.25
• C. 3.5
• D. 4.5

Answer 1

The correct option is C 3.5

Modal class is $3-4$ since it is the class with highest frequency.

$Mode=l+\left[\frac{f_1-f_0}{2f_1-f_0-f_2}\right]\times h$
$f_1$ represents the frequency of the modal class.
Also,
$l=$lower boundary of the modal class
$h=$ size of the modal class interval
$f_0=$ frequency of the class preceding the modal class
$f_2=$ frequency of the class succeeding the modal class

Here, $f_1=25,f_0=16,f_2=16,l=3,h=1$

$Mode=3+\left[\frac{25-16}{2\times 25-16-16}\right]\times 1$

$\therefore Mode=3.5$