# How do the different measures of center compare?

Feb 18, 2015

There are three main center measures.

The mean or average is calculated from the sum of all values divided by the number of cases. It gives - as the word says - an idea of the average. Disadvantage is, that it is susceptible to extreme values. Example: Average income of a group of 1000 people is 500 a week. Add a person who gets 100000 a week and see what happens to the average.
$500000 / 1000 = 500$
$600000 / 1001 \approx 599$

The mode is the value or class value that happens most. It is the 'bump' in your frequency distribution. You have a problem if there are more bumps.

The median is the value, of which half the population has a lower value, and half a higher. It is the value of 'the middle man' if you order your cases by value. Greatest advantage of using median, is that it is hardly susceptible to extremes. You might try the above example with the median.

In a perfect, or allmost perfect, normal distribution, these three are the same.