Question

A friend of yours is new to statistics and wants to find the middle of their data. They know something about the median and mean being those middles, but doesn't know which to use and when. Help your friend by explaining to them:

What is the median
What is the mean
In which situations should use the median instead of the mean.
Any other helpful tips you may think about when it comes to Measures of Central Tendency

Answer 1

Ask your math teacher, he's a nice guy and would like to help you.

Explanation:

-Find his email on course home page

-Compose new email

- Ask your question or come to a help session

Answer 2

I think it helps to look at an example.

Let's say we had the set {1,2,3,4,55}

The median is the middle most number. In this case it would be 3. There are the same number of values on either side of 3.

The mean is found by adding up the numbers and then dividing by 5 (which is the number of values). The mean is (1+2+3+4+55)/5 = 13

Notice that the median (3) is much closer to the main cluster {1,2,3,4}; whereas the mean (13) is trying its best to be somewhere between that main cluster and the outlier of 55. The mean is pulled by the outlier as if it was a gravitational or magnetic pull.

As such, the mean is a bad measure of center when outliers are present. The larger the outlier, the worse the representation. This is why home prices for instance rely on the median. Multi-million dollar mansions greatly skew the mean housing price to be (much) larger than it should be.

If there aren't any outliers, then the mean is a better measure of center because it involves each item weighing in.