Question

Find the mode of the given data.

$$\begin{array}{cc}\text{Class}& \text{Frequency}\\ 0-5& 200\\ 5-10& 250\\ 10-15& 225\\ 15-20& 300\\ 20-25& 275\end{array}$$

• A. 18.25
• B. 18.5
• C. 18.75
• D. 19.75

Answer 1

The correct option is C 18.75

Modal class is 15-20 since it is the class with highest frequency.

Now, $f_1$ = 300, $f_0$ = 225, $f_2$ = 275, I = 15, h = 5

$Mode=l+\left[\frac{f_1-f_0}{2f_1-f_0-f_2}\right]\times h$
$f_1$ 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

$Mode=15+\left[\frac{300-225}{2\times 300-225-275}\right]\times 5$

$\therefore Mode=18.75$