Question

Show that the mean median and mode are equal??

Answer 1

There are some data sets where the values of the mean, median, and mode are equal. But for the most part, they aren't.

Explanation:

Let's first talk about what these are:

• mean is the sum of the values divided by the count of the values
• median is the "middle term" when the values are lined up in ascending (or descending) order
• mode is the value(s) that is/are have the highest count (and greater than 1)

I can create a sample data set where all three of these are equal:

`1,2,3,3,3,4,5`

and the mean, median, and mode all equal 3.

But if I change this, even a little bit, one or more of the measures are going to change:

`1,2,2,3,3,3,4,4,5`

Now the mean and median are 3 but the mode is 2, 3, and 4.

`1, 2, 3, 4, 5`

The mean and median are still 3 but now there is no mode.

`1, 2, 3, 5, 6`

Now the median is 3, the mean is `17/5`, and there still is no mode.