Measures of Central TendencyMeasures of Central TendencyThe term central tendency refers to the "middle" value in a group of data. The "middle" value depends on the measure you choose to use: it is most commonly measured in statistics by using mean, median, and mode. A quick definition for all three with a simple example can be found on the vocabulary page.
MeanThe mean is the measure of central tendency used most often in statistics. The word "average" usually refers to the mean or arithmetic mean. The mean is the sum of all the data values divided by the total number of data values. For example: |
Practice calculating a simple mean, median, and mode at Dr. Ufigure's Simple Statistics Tutorial.
For a more complete mathematical explanation, including formulas, try the QuickMBA tutorial site. |
In common English usage, median means something in the middle, like the grassy strip in the middle of a boulevard or freeway.
Similarly, in statistics the median is the middle value when you sort all your data from lowest to highest (or highest to lowest). For example, to find the median in the set below, we need to do several steps:
| Original Data
5, 7, 3, 10, 8 |
|
| Step 1:
arrange all the data from lowest to highest |
Sorted Data
3, 5, 7, 8, 10 |
| Step 2:
count the number of data points in the list |
there are five (5) data points |
| Step 3:
the median is the middle |
3, 5, 7, 8, 10
median = 7 |
If there are an even number of data points, then there is no single data point at the exact middle. In this case, the median is calculated by taking the mean (average) of the two points closest to the middle. For example, if the data is 2, 5, 6, 7 (four data points - an even number) then the numbers closest to the middle are 5 and 6. The median is the average of 5 and 6 = (5 + 6)/2 = 11/2 = 5.5
Notice that when you have an even number of data points, the median is not usually one of the data points.
The mode is the most frequently occurring value in the data set. A data set can have more than a single mode - this is called multimodal. To find the mode in a set of data, sort all your data from lowest to highest (or highest to lowest) and look for repeats. The most points are the mode. Here is an example:
| Original Data
4, 9, 6, 3, 5, 4 |
|
| Step 1:
arrange all the data from lowest to highest |
Sorted Data
3, 4, 4, 5, 6, 9 |
| Step 2:
look for repeats |
3, 4, 4, 5, 6, 9 | Step 3:
the mode is the points that occur the most |
3, 4, 4, 5, 6, 9 mode = 4 |
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