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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.

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.

$Mean=Number of ValuesSum of Values $

The mean of a set of numbers $x_{1},$ $x_{2},$ $…,$ $x_{n}$ is generally denoted as $xˉ.$

$xˉ=nx_{1}+x_{2}+…+x_{n} $

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.

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

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.
*does not* have a mode.

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