Question:
The mode of the continuous frequency distribution given in the following table is:
The mode of the continuous frequency distribution given in the following table is:
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The modal class is the class having the highest frequency.
Updated On: Jun 12, 2026
- $65.75$
- $67.50$
- $68.75$
- $66.25$
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The Correct Option is D
Solution and Explanation
Concept:
For grouped data,
$$
\text{Mode}
=
L+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)h
$$
Step 1: Identify the modal class. The highest frequency is $12$, corresponding to the class $65-70$. Thus, $$ L=65,\quad f_1=12,\quad f_0=9,\quad f_2=3,\quad h=5 $$
Step 2: Substitute into the formula. $$ \text{Mode} = 65+\left(\frac{12-9}{24-9-3}\right)\times 5 $$ $$ = 65+\left(\frac{3}{12}\right)\times 5 $$ $$ = 65+\frac{5}{4} $$ $$ = 66.25 $$ \[ \boxed{66.25} \]
Step 1: Identify the modal class. The highest frequency is $12$, corresponding to the class $65-70$. Thus, $$ L=65,\quad f_1=12,\quad f_0=9,\quad f_2=3,\quad h=5 $$
Step 2: Substitute into the formula. $$ \text{Mode} = 65+\left(\frac{12-9}{24-9-3}\right)\times 5 $$ $$ = 65+\left(\frac{3}{12}\right)\times 5 $$ $$ = 65+\frac{5}{4} $$ $$ = 66.25 $$ \[ \boxed{66.25} \]
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