Briefly |
A measure of center (such as the mean) is a statistic that gives you a value for an attribute that represents the entire population or a group. |
Here are two common measures of center:
mean |
The "average" value: add up all of the values and divide by the number of values. In Fathom, use the mean( ) function |
median |
The "middle" value: sort the values and choose the middle one. If there are an even number of values, take the mean of the middle two. In Fathom, use the median( ) function |
Example: the numbers of tornadoes in the state during five successive weeks are {4, 20, 1, 3, 2}. The mean is 6 and the median is 3.
We call median a "resistant" measure because it is resistant to the effects of outliers. In the example, if the 20 were 100, the mean would be 21--but the median would not change.
Choose your measure according to what you need to do with it. To estimate the total number of tornadoes you would get during a four-week period a year from now, use the mean. On the other hand, the median is a more "typical" value. Here are some observations about choosing a measure of center:
Use the mean when you need to compute an expected value.
If there are many repeated values, a mean may distinguish two groups when a median does not.
Median is often better when a distribution is greatly skewed (as long as it doesn't have too many repeated values).
People tend to use median for "money" things such as home prices or salaries (perhaps because the distributions are skewed). For example, the mean home price will be high compared to most people's houses.
People tend to use mean for measurements and scores: height, weight, SAT tests, etc.
There are other measures of center. One example is in skating or diving judging, where they use a trimmed mean: Throw away the high and the low--and then average.