Question

Find the mode of the following frequency distribution:

Class	$25-30$	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$
Frequency	$25$	$34$	$50$	$42$	$38$	$14$

Answer 1

Finding the mode:

$\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathbf{=}\mathit{l}\mathbf{+}\frac{{\mathbf{f}}_{\mathbf{1}}\mathbf{-}{\mathbf{f}}_{\mathbf{0}}}{\mathbf{2}{\mathbf{f}}_{\mathbf{1}}\mathbf{-}{\mathbf{f}}_{\mathbf{0}}\mathbf{-}{\mathbf{f}}_{\mathbf{2}}}\mathbf{}\mathbf{\times }\mathbf{}{\mathit{h}}^{}$

Where l = Lower limit of the class interval

$f_1$ = Frequency of the modal class

$f_0$ = Frequency of the class preceding the modal class

$f_2$ = Frequency of class succeeding the modal class

$h$ = size of the class interval

In the given frequency distribution, $35-40$ will be the modal class because this class has the maximum frequency. Therefore,

$l=35$, $f_1=50$, $f_0=34$, $f_2=42$, $h=5$

Substitute the values in the formula of mode we get,

$$\begin{gathered} Mode=35+\frac{50-34}{2\times 50-34-42}\times 5 \\ =35+\frac{80}{24} \\ =38.33 \end{gathered}$$

Final Answer: The mode of the given frequency distribution is $\mathbf{38}\mathbf{.}\mathbf{33}$.