There is often a need to describe a collection of data (a data set). One way to do this to find the middle value. This is called the average or sometimes the measure of central tendency. Below are examples of three types of average; arithmetic mean, median, and mode.
The examples below will show how to calculate the arithmetic mean, the median, and the mode for the following set of values showing the heights of students in a 6th Grade class.
Student Heights (cm)
Sometimes just the term "mean" is used. There are other types of "mean" so, to be precise, we should say "arithmetic" mean. The arithmetic mean is calculated by taking the sum of all values and dividing by the number of values. The examples below show this.
Example 1: The Arithmetic Mean
|=||sum of the values|
|number of values|
|=||(135 + 154 + 154 + 152 ....)|
Note: Arithmetic Mean does not always provide the best description of the middle of a set of data. For example, in a sports team, if one or two superstars are paid much more than the rest of their team mates, then they will "skew" the data.
The Median is the value that separates the lower half from the upper half of a data set. In other words, if the values are sorted in order, the median will be the value in the middle. If there are an odd number of values the median is obvious. If there an even number of values, the median is calculated by taking the arithmetic mean of the two middle values.
Example 2: The Median
First, order the data from smallest to largest.
Student Heights (cm)
There are 25 values. The median is therefore the 13th value. There are 12 lower values and 12 higher values.
The median of the data is 149 cm
The Mode is the value that appears most often in a data set
Example 3: The Mode
It is often easier to find the most occurring value after sorting and ordering the data (which you have to do anyway if you are also looking for the median).
There are four occurrences of the height measurement of 152cm. The next most common values are 140, 146, 149, and 154 which all occur two times.
The mode is 152 cm.