Math Practice: The Difference Between Range, Mean, Mode, and Median

When you have a group of numbers, there are a few different ways to study them. Some of these ways include mean, mode, and median. Although, many people also like to calculate the range. Let’s pretend you’re a teacher with a set of test scores that you would like to analyze. We can learn more range, mean, mode, and median using the following set of numbers:

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      72   96   72   88   91   67

Mean

As the teacher, you may decide to determine what the mean, or average, was for your students. This could tell you how well the class did overall.

To calculate the mean, add up all the numbers. Then, take the sum and divide that by the number of numbers that you added. So, let’s practice. First, add all the numbers together:

72 + 96 + 72 + 88 + 91 + 61 = 486

Then, count the numbers that you have. (This set has 6 numbers.) So, the next thing you need to do is divide the sum by 6.

486/6 = 81

Therefore, the mean is 81.

Mode

The mode is simply the value that occurs the most often. If there aren’t any repeated numbers, then there is no mode. However, you can also have multiple modes if there are more than one number that is repeated the same amount of times.

With our set of numbers, the mode is 72 since there are 2 in the list. The rest of the numbers are only listed once, so there is only one mode.

Median

The median refers to the middle number. It should have the same amount of numbers greater than the median and less than it. To determine the median, you need to reorder the numbers from smallest to largest. So, for our numbers, the list should be:

      67   72   72   88   91   96

Since there is an even amount of numbers, you’ll have to take a few more steps. After identifying the two middle numbers (72 and 88), you need to take the average (mean) of these numbers. So,

72 + 88 = 160

Then, divide the numbers by 2:

160/2 = 80

As a result, the median for this set of numbers is 80.

Range

The range is the difference between the largest number and the smallest one. So, after identifying them, subtract the smallest number from the largest. For example:

96 – 67 = 29

The range of these numbers is 29, showing the difference between the top and bottom scores.

Range, Mean, Mode, and Median: Math Practice

Could you calculate the range, mean, mode, and median on your own? Try it for yourself with the following set of numbers:

      27   33   44   48   45   38   45

Check your answers below. How did you do? Do you have any other questions about calculating the range, mean, mode, and median? Let us know in the comments below.

Answers

Mean: (27 + 33 + 44 + 48 + 45 + 38 + 45)/7 = 40
Mode: 45
Median: 27  33  38  44  45  45  48 = 44
Range: 48 – 27 = 21

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