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Mean, Median, and Mode: Defining Averages in Math

Mean median and mode: teenanger sitting on a sofa and doing her homework

Mean, median, and mode are three ways of describing data sets. The mean and median measure central tendency, or the average amongst a set of numbers. The mode is the most commonly occurring number.

If you’re a little confused, don’t worry. We’re here to unpack the definitions of mean, median, and mode.

What Is Mean, Median, and Mode?

Mean, median, and mode are all considered measures of central tendency. This means that they help us identify the single number that best represents the wide range of values within a given set of data. Let's use this set of data to demonstrate:

set of data

In your data set above, you can see that the smallest value is 5 and the largest value is 38. You can use three methods to find the average value within this list of numbers: mean median mode. Let's define each method.

Mean

Also called an arithmetic mean or average value, the mean of a data set is the sum of all the numbers divided by the number of data points there are within the set. When you are finding the mean of a specific sampling of data, for example, when finding a population mean, it is called a sample mean.

Let's explain how to find the mean of the data set above. The first step is adding all the numbers of the data set together:

Mean median and mode: add the set of data

Next, we need to count the number of values within the set:

count the numbers

Now, let's divide the sum by the count to get the mean:

Mean median and mode: mean

Median

To find the median of a set of data, you’ll separate the lower half of values from the upper half of values and determine the middle value. Let's walk through the process of finding the median:

The first step is arranging the data set in numerical order, starting with the smallest number and ending with the largest number:

arrange the data numerical order

Now, separate the lower half from the upper half. To make the lower and upper halves equal, each will have four numbers. The leftover middle number will be the median:

Mean median and mode: median

If there are two numbers in the middle of the set, you must add these numbers and divide by two to get your median.

Mode

The mode of a set of numbers is the most common number within the set. Here is a mode example:

common number example

You must choose the most frequent number within this set. Since the number of times 22 occurs is three, this value is the mode:

Mean median and mode: mode

Using Mean, Median, and Mode

Finding the mean, median, and modes of a set of numbers are useful ways to measure averages. Whether you need to find the exact average number (mean), the middle-most number, or the most common number within a set (mode), you can use one of these three methods to determine central tendency.

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