Question

Which of the following statements are correct about mode?

• A. If all the given values in a data set occur twice, then the data is said to be bimodal.
• B. If a dataset have three modes, then the given data set is said to be trimodal.
• C. If all the values of the given data set occur for the same number of time, then the data set is said to have no mode.
• D. None of the above.

Answer 1

Answer: (B), (C)

If all the values of the given data set occur for the same number of time, then the data set is said to have no mode.

For bimodal data, consider the following data set:


Here, there are two values i.e. $15\&20$ which occur for the maximum number of times, thus the given data set has two modes and is called bimodal.

Similarly, if three different values occur for the maximum number of times, then the data set is said to be trimodal.

But this is not possible if all the data values occur equal number of times.

Consider another example,


In this data set, each of the given value occurs for the same number of times, thus by definition this data set is said to have no mode.