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## 6th grade (Illustrative Mathematics)

### Course: 6th grade (Illustrative Mathematics)>Unit 8

Lesson 7: Lesson 9: Interpreting the mean as fair share

# 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.
Find the mean number of bananas each of the monkeys has in the picture below.
bananas

## 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 $\left\{7,2,8,6,7\right\}$:
$\begin{array}{rlr}7+2+8+6+7& =30& \text{Step 1}\\ \\ \\ \\ \frac{30}{5}& =6& \text{Step 2}\end{array}$
The mean of this data set is $6$.

## Calculating the mean walkthrough

Let's find the mean of the data set $\left\{2,1,2,4,5,4\right\}$ together.
Add up all of the data points.

How many data points are in the data set?

Great! Now divide the total by the number of data points.
The mean of this data set is
.

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

## Practice

Find the mean of the data set $\left\{5,23,8,12\right\}$.

Find the mean of the data set $\left\{2,7,5,4,6,3\right\}$.

Find the mean of the data set $\left\{4.5,5,3.5,2,2.5\right\}$.

## Want to join the conversation?

• how would you know when an outlier affects a data set?
• 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.
• How about the range? What is it?
• 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.
• 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. >_<
• Your teacher wants you to be very proficient in this I guess but now you can do it in a snap
• is coculating the mean hard or easy vote up for easy vote down for no
• this are so hard sorry I'm not good with math
• 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!