Main content

## Get ready for AP® Statistics

# Calculating the mean

Learn how to calculate the mean by walking through some basic examples & trying practice problems.

The mean is used to summarize a data set. It is a measure of the center of a data set. Let's look at an example.

Claire has 5 cookies, Brooke has 3 cookies, Deandra has 6 cookies, and Lucy has 2 cookies. Find the mean number of cookies.

Let's start by drawing a picture to show each person and their cookies:

Imagine that the girls combined all of their cookies

and then each took the same number of cookies.

Each girl would have 4 cookies. So, the mean is 4 cookies.

**Key idea:**We can think of the mean as the number of cookies each girl would have if they were equally distributed among the four girls.

## Calculating the mean

We don't need to draw a picture every time we want to calculate the mean. Instead, we can follow these steps:

**Step 1: Add up all of the data points**(this is like combining all of the cookies)

**Step 2: Divide the total by the number of data points in the data set**(this is like each girl taking the same number of cookies)

Let's do this for the data set left brace, 7, comma, 2, comma, 8, comma, 6, comma, 7, right brace:

The mean of this data set is 6.

## Calculating the mean walkthrough

Let's find the mean of the data set left brace, 2, comma, 1, comma, 2, comma, 4, comma, 5, comma, 4, right brace together.

Great! Now divide the total by the number of data points.

Now it's time to try some practice on your own.

## Practice

## Want to join the conversation?

- how would you know when an outlier affects a data set?(56 votes)
- An outlier is a number that is far from the data set. This could be the case such as in this set:

158, 156, 85, 145, 157, 159. 85 is the outlier. Without the 85 the mean would be 155, but with the 85 the mean is about 143. Just one number makes the mean decrease by 12. An outlier always affects a data set, because an outlier is a number that is nowhere near the current set of numbers.(24 votes)

- How about the range? What is it?(20 votes)
- The range of a numerical set is just the difference of the largest and smallest numbers. For example, lets say we have a set: {1, 4, 2, 9, 10} We will take the largest number, 10, and the smallest number, 1, and find the difference. 10-1=9. Therefore, the range of the set is 9. Hopefully this helps you understand range any better.(53 votes)

- this are so hard sorry I'm not good with math(5 votes)
- I would suggest keeping a notebook with all the math facts you have learned. Try to really get stuff pounded into your brain before you move on. For this you can use the rhyme: Hey diddle didle, the medians the middle, you add and divided for the mean, the mode is the one that appears the most, and the range is the difference between. Never skip stuff or guess randomly. Try to make sure you REALLY understand the answer. It might take a bit longer, but it's worth it in the long run. Also, don't be afraid to ask for help. I struggle with math, too. But just keep trying and I promise you'll get it. Also, just take a deep breath. It can get hard if you're super stressed. And I like to type out what I'm thinking, so if there is a problem, my teacher can figure out where I went wrong and correct it from there. Keep it up!(27 votes)

- My teacher gives me this one like eighty times a day so I know all the answers but she still keeps giving it to me. >_<(11 votes)
- Your teacher wants you to be very proficient in this I guess but now you can do it in a snap(5 votes)

- Can there be more than one mode?(5 votes)
- As you probably know, mode is the biggest set of ungrouped data. If two sets of data have the same amount, but the other data is less than the data that they have, then both of them are the modes. This is also true with 3 modes, 4 modes, 5 modes and so on.(3 votes)

- How will you find the range?(4 votes)
- The range is the difference between the highest number and the lowest number in the set, so for example lets say we have the set {10, 5, 3, 15, 25}.

The lowest number here is 3 and the highest number is 25, so the range will be 25 - 3 which is equal to 22.(3 votes)

- is there other ways to do this(5 votes)
- can you please like my other one because if you don't my mom will kill me(5 votes)
- You have seen my previous question,
`I've just found out that the`

*mean, median,*and*mode*are the same in the data set`3, 5, 5, 7`

.

Can you have the range, mean, median, and mode be all the same in a data set?

Since`7-3=4`

, the data set above will not work as a note.

Is it possible for this to be true if you have more than 4 numbers instead?(3 votes)- Yes, 2.5, 5, 5, 5, 7.5

also 2.5, 3, 5, 5, 7, 7.5

There are many other potential data set with the given properties.(6 votes)

- Thanks for the lesson Khan because I am learning 5th grade math so l can avoid summer slide in fourth grade summer.😋😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀😀(5 votes)