Example 2.28 from Statistics, 2.5 Measures of the Center of the Data

Measures of the Center of the Data: example 2.28

Suppose that in a small town of 50 people, one person earns $5,000,000 per year and the other 49 each earn $30,000. Which is the better measure of the center: the mean or the median?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\bar{x} = \frac{5, 000, 000 + 49 (30, 000)}{50} = 129,400$
M = 30,000
There are 49 people who earn $30,000 and one person who earns $5,000,000.

The median is a better measure of the center than the mean because 49 of the values are 30,000 and one is 5,000,000. The 5,000,000 is an outlier. The 30,000 gives us a better sense of the middle of the data.

How did it go?

Solution

Solution