Question

Choose the correct option regarding the mode of a data set.

Statement I : Numerical data can have a mode but categorical data cannot have a mode.

Statement II : The mode is always one of the values of the data set.

• A. Only statement I is wrong.
• B. Only statement II is wrong.
• C. Both the statements are correct.
• D. None of the statements are correct.

Answer 1

The correct option is A Only statement I is wrong.

Let's take an example to understand the provided statements.

Consider the following data set of alphabets:

$\text{D}$

$\text{C}$

$\text{B}$

$\text{C}$

$\text{A}$

After arranging the above data set in alphabetical order, we get

$\text{A}$

$\text{B}$

$\text{C}$

$\text{C}$

$\text{D}$

We can make the corresponding frequency table as Frequency Table

Alphabet	Frequency
$\text{A}$	$1$
$\text{B}$	$1$
$\underset{–}{\text{C}}$	$\underset{–}{2}$
$\text{D}$	$1$

From the above frequency table, we find that the alphabet $\text{C}$ is occuring the most number of times in the data set.

Hence, the mode of the data set is $\text{C}$.

Here, the data set $\text{{D, C, B, C, A}}$ contains non-numerical characters, i.e., it is a categorical data, which has the mode as $\text{C}$.

Secondly, the mode $\text{C}$ is a character that is present in the considered data set $\text{{D, C, B, C, A}}$.

Therefore, we can conclude
$\bullet$ Both categorical and numerical data can have a mode.
$\bullet$ The mode is always one of the values of the data set.

$\therefore$ Statement I is wrong, whereas statement II is correct.