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Measures of Center

A measure of center, or a measure of central tendency, is a statistic that summarizes a data set by finding a central value. The most common measures of center are mean, median, and mode. These are often used together with a measure of spread. They give an idea of both what a typical value is and how much the data can be expected to deviate from it.
Interactive applet where points of the dot plot can be moved around.
Move the points around in the dot plot to generate new data. The applet tells the mean, the median, and the mode of the data set.



The mean, or the average, of a numerical data set is one of the measures of center. Mathematically, it is the sum of all of the data values divided by the number of values in a data set.

The following applet calculates the mean of the data set on the number line. Points can be moved to change the data values.
The mean of a set of numbers is generally denoted as

There are several types of the mean in statistics, for example population mean or geometric mean. Therefore, the exact name of the considered mean is the arithmetic mean. However, for simplicity, the shortened name is usually used.



The median is a measure of center that lies in the middle of a data set when the data set is written in numerical order.

Odd Number of Data Points

Consider an odd number of data points in a data set. There is only one value in the middle, and that is the median.
Random data set with 9 elements, the median is marked

Even Number of Data Points

Next, consider an even number of data points in a data set. The median is the average of the two middle numbers.

Random data set with 10 elements, the median is marked



The mode is a measure of center that shows the most common value in a data set. This can be used for both numerical and categorical data.
Random data set with 11 elements, the mode is marked
When there are two or more data values that are just as common, there can be more than one mode. However, if all values only occur once, then the data set does not have a mode.