May I know if the distribution you are working on is discrete or continuous?

Dear Dreamlee Sharma,

I have made the question more clear that is given below.

"If a given data set has no mode then what can be concluded about the empirical relationship among mean, median and mode of the data set?

Similarly, if a distribution (discrete or continuous) then what can be concluded about the empirical relationship among mean, median and mode of the distribution ? "

Now, think on the question try for its answer.

A set of data (sample) may or maynot have a mode, but it doesn't mean that the population from which the set of data has been collected, has no mode. I think a distribution will always have a mode, either in closed form expression or not. Here distribution means probability distribution. can you give me an example of a distribution without a mode?

@ Dreamlee Sharma ,

It is true the following statement:

" If a set of data contained in a sample drawn from a population (or in other words if a sample drawn from a population) has no mode, this does mean that parent population has no mode."

However, it is not true that a distribution will always have a mode. For example, the uniform distribution has no mode.

Dear Sir, if a set of data drawn from a population, has no mode, it doesn't mean that the parent population has no mode. The mode of a uniform distribution, U(a, b) is any value between a and b. Similarly for a standard uniform distribution, any point in the interval 0 and 1 are its mode. It is not necessary that only a non rectangular distribution will have a mode. Even a rectangular distribution has mode.

Regards

Dreamlee Sharma