Question

Consider the following statements:

Statement I: The data set is said to have no mode if all the values occur for the equal number of times.

Statement II: The data set cannot have more than one mode.

With respect to the mode of the data set, choose the correct option.

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

Answer 1

The correct option is C Only Statement I is correct.

If all the data points in the data set occurs for the equal number of times, then the data set is said to have no mode.

Consider the following data set, which depicts the number of pets each friend of a group of $5$ friends has


Since each friend has equal number of pets, therefore this data set is said to have no mode.

On the other hand, when the data set contains two or three values that occur for the same number of times, then the data set is said to be bimodal or trimodal respectively.

For example, consider the following data which depicts the scores of $5$ students in a quiz,


Here, it can be observed that there are two students with score $11$ and two students with score $12$. Thus, the given data set is bimodal with modal values $11$ and $12$.

So, option (c) is correct.