Difference between Mean, Median, and Mode

Updated on June 28, 2017

To a regular person whose major is not math, there’s only one type of “average.” It’s the one that can be determined by adding all the numbers up in a series and then dividing the total by the number of values (for instance, the average of the numbers 1, 2, and 3 is 2).

Guess what? That’s not the only type of “average” there is in statistics. In fact, there are three: the mean, median, and mode. Sure, you remember these terms from your math class in high school, but do you remember what they are exactly? In this article, we will give you a quick refresher on this topic.

Descriptions

Mean

The mean is what we call the “average” in layman’s term. It can be calculated by getting the sum of all the given numbers and then dividing the total by the number of values there are in the given set.

Let’s take a look at some examples below:

  • The given numbers are 78, 24, 56, 47, 32, 18, and 90. To get the mean, we get the sum of all the values: 78 + 24 + 56 + 47 + 32 + 18 + 90 = 345. Then we divide the sum by the number of values in this set: 345 ÷ 7 = 49.29. The mean is 49.29.
  • The given numbers are 12, 12, 12, 8, 1, 17, 21, and 21. To arrive at the mean we add them up: 12 + 12 + 12 + 8 + 1 + 17 + 21 + 21 = 104. We then divide the sum by the number of items: 104 ÷ 8 = 13. The mean is 13.

Note that the mean does not always have to be a value from the given set of numbers and is not always a whole number (it can be a decimal).

The median is the middle value of a set of numbers. To get the median, list the numbers in ascending order, then find the middle value. Half of the numbers are lower than the median and the other half are higher than the median.

Let’s look at some examples:

  • The given numbers are: 78, 24, 56, 47, 32, 18, and 90. Let’s rearrange in ascending order first: 18, 24, 32, 47, 56, 78, 9. Then find the middle value, which is 47. So the median is 47.
  • The given numbers are 12, 12, 12, 8, 1, 17, 21, and 21. Let’s rearrange: 1, 8, 12, 12, 12, 17, 21, 21. In this example, we have an even number of values, which means we have two middle numbers. If this happens, find the mean (the usual average) of the two middle values (in this case 12 and 12). So, it is 12 + 12 = 24 and then 24 ÷ 2 = 12. The median for this set of numbers is 12.

It is possible for the median and mean to have the same values.

Finally, the mode is the number that is repeated more often than any other value in the same list.

Let’s look at a couple of examples:

  • The given numbers are 12, 12, 12, 8, 1, 17, 21, and 21. The most commonly occurring value in this set is 12 (we have three twelves in this example). Therefore, 12 is the mode.
  • The given numbers are: 78, 24, 56, 47, 32, 18, and 90. None of the numbers are repeated, so this set does not have a mode.

It is also possible to have more than one mode in a given set. This happens when two or more values have the same number of repetitions. For example:

  • The given numbers are 1, 1, 1, 4, 4, 4, 6, 6, 8, 8, 8, 5, 5. Notice that the numbers 1, 4, and 8 are all repeated three times. In this case, we have three modes: 1, 4, and 8.
  • The given numbers are 77, 77, 44, 55, 55. We have two modes in this example, which are 77 and 55.

Mean vs Median vs Mode

What, then, is the difference between mean, median, and mode?

The mean is the “usual average.” It can be calculated by adding all the numbers up and then dividing the sum by the number of values in a set. The median is the middle number which can be determined by arranging the numbers in ascending order first and then picking the middle value (if there are an even number of values, the mean of the two middle values is the median of the set). The mode, on the other hand, is simply the most frequently repeated number in a given set (there can be multiple modes or none at all).

Comparison Chart

MeanMedianMode
The “usual average”; add all the numbers then divide the sum by the number of values in a setThe middle number; arrange the numbers in ascending order then pick the middle value (if there are an even number of values, the mean of the two middle values is the median)The most frequently repeated number in a set; a set can have multiple modes or none at all