# GED Mathematical Reasoning: Mean, Median, Mode and Range

- Data is information that is presented in an organized way, usually using a list, table or graph. When analyzing data, mathematicians are interested in two characteristics. The first is called central tendency or the typical value. The second is called variation or spread.
- In this chapter, we’ll focus on the first characteristic and talk about how to describe the typical value. One way to do so is by calculating the mean of the set of data. The mean is the average value. Calculating the mean or average is a two step process. First, add all the values. Then, divide the sum by the number of values in the set.
- The median is the middle value when the values have been placed in order. If there is an even number of values, then the median is the average of the two middle values. It follows, then, that the first step in finding the median is to put the data values in order and it is common to put the values in order from smallest to largest.
- The third way to describe the typical data value is called the mode. The mode is the data value that occurs most often in the data set. A data set may have one mode, more than one mode, or no mode at all.
- One way to measure how much a set of data varies or how spread out the data values are, is by finding the range. The range is the difference between the largest value and the smallest value. In other words, the higher the range, the more varied or spread the set of data.

**Example 1**

What is the mean (or average) score of the four test scores listed below?

The test scores are:75, 82, 95, 86

To find the mean or average of the set of test scores given in this example, we’ll first add the values.

Now, we’ll divide the sum by 4, since there are four values in the data set.

Therefore, the mean or average of the test scores is 84.5.

**Example 2**

What is the median score of the four test scores listed below?

The test scores are:75, 82, 95, 86

Since we have an even number of values, there is not one single middle value so we’ll find the average of the two middle values. To do this, add 82 and 86 and then, since we’re adding two values, we’ll divide the sum by 2. 82 plus 86 equals 168. Then, 168 divided by 2 gives a median of 84.* *

**Example 3**

What is the mode of the following set of data?

The data values are: 12, 15, 13, 12, 19

In the data, each value occurs one time except for the value 12, which occurs twice. Therefore, the mode is 12.

**Example 4**

What is the range of the following set of data?

The data values are: 12, 15, 13, 12, 19

To find the range of the data, it is helpful to first put the values in order from smallest to largest. After doing so, we have: 12, 12, 13, 15, and 19

Now, to find the range we’ll subtract the smallest value from the largest value. So we’ll compute: 19 – 12 = 7. So the range is 7.