Reference

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 the mean, median, and mode. Measures of center are often used together with a measure of spread to 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 identifies the mean, median, and mode of the data set.

Concept

Mean

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

Mean=Sum of Values/Number of Values

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 x_1, x_2, ..., x_n is generally denoted as x.

x=x_1+x_2+⋯+x_n/n

There are several types of the mean in statistics, such as population mean and geometric mean. The exact name of this mean is the arithmetic mean, but it is often shortened to the mean for simplicity.

Concept

Median

The median is a measure of center that lies in the middle of a numerical data set when the data set is written in numerical order. When the the data set has an odd number of data points, the median is the value in the middle.

However, when the the data set has an even number of data points, the median is the average of the two middle numbers.

Random data set with 10 elements, the median is marked

Concept

Mode

The mode is a measure of center that shows the most common value in a data set. Modes can be used for both numerical and categorical data.

A data set can have more than one mode if two or more data values are equally common. However, if all values in the set only occur once, then the data set does not have a mode.