## What are the differences between Mean, Median, and Mode?

Mean, Median, and Mode are three of the different ways to work statistical problems. Let’s start with mean. Mean just means the average. For example when someone says the average of the two numbers 20 and 40 is 30, they are referring to the mean. The best way to help you understand how to find the mean is to take all of the numbers you want to find the average for and add them together. Next, you will want to divide your total by the number of items you added.

### Example 1: Find the mean (average) for the following numbers: 10, 58, 18, 34, 35, and 21.

**Step 1:** Add all of the numbers together

10 + 58 + 18 + 34 + 35 + 21 = 176

**Step 2:** Divide the total from step 1 by the number of items added together, so in this case we would divide by 6 because we added together 6 numbers.

176/6 = 29.33

### Example 2: Find the mean (average) for the following numbers: 9, 10, 11, 20, 14, 15, 18, 7, and 5

**Step 1:** Add all of the numbers together

9 + 10 + 11 + 20 + 14 + 15 + 18 + 7 + 5 = 109

**Step 2:** Divide the total from step 1 by the number of items added together

109/9 = 12.11

## Median

Now for finding the median. When you think of median you think of the word medium, right? When you go to get a drink at a restaurant, they usually have three options: small, medium, or large. The medium option is smack dab in the middle and that is exactly what median means. It means the middle value.

It is easy to find the median value in a set of numbers with an odd number of values. For example, the median (middle) value of the set (1,2,3,4,5) is 3. The answer is 3 because it is smack dab in the middle. But what about for an even number set???

If you are trying to find the median for the set (1,2,3,4), you don’t have a middle value, so you will have to find the average of the two numbers in the middle, which are numbers 2 and 3. Remember to find the average you add the number together ( 2 + 3 = 5) and then divide total by the number of items (5/2 = 2.5). Your answer is 2.5, which is your median for this example.

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### Example 1: Find the median (middle) for the following set of numbers: 4, 7, 10, 11, 15, 18, 21

**Step 1:** Make sure all numbers are in numerical order (they are! :))

**Step 2:** Find the median number (middle)

Because it is an odd set of numbers, the middle value is 11. No more work needed! WOO HOO

### Example 2: Find the median (middle for the following set of numbers: 12, 9, 10, 4, 21, 22, 18, 26

**Step 1:** Make sure all numbers are in numerical order

Re-ordering of numbers = 4, 9, 10, 12, 18, 21, 22, 26

**Step 2:** Find the median number (middle)

This is an even set of numbers. Because of this, we have two middle numbers: 12 and 18. We now need to find the average of these two numbers:

12+18 = 30

30/2 = 15 — The median is 15

## Mode

The last thing to understand is the mode. The mode is the most frequently occurring value in a set of numbers. It is common to have 2 or more different numbers occurring the same number of times and in that case you would have multiple modes.

The easiest way to explain modes is to practice example problems.

### Example 1: What is the mode of the set: 1,3, 3, 5, 5, 7, 9, 10, 10, 10, 11, 11

**Step 1:** Find the number or numbers that occurs more frequently than any other number in the set of numbers.

**Answer:** 10, because is occurs 3 times in the above set, which is more than any other number listed

### Example 2: What is the mode of the set: 5, 5, 10, 20, 20, 30, 40, 50

**Step 1:** Find the number or numbers that occurs more frequently than any other number in the set of numbers

**Answer:** 5 and 20, because both numbers occur 2 times in the above set, which is more than any other number listed.

## Side Note

You may be wondering why anyone would want to use the median over the average? The answer is because the median gives a more accurate depiction of the true middle number. If you only use the mean (average), you could get a slightly higher number than using the median.

For example, the average income in the United States might be $50,000 even though most people make way less. Thousands of people with $20,000 incomes are balanced out by a few people who make in the millions. This is an example where you would want to use the median over the mean (average).