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Learning how to find the 'average' of a data set to describe its center.
If you and four friends all had different amounts of candy, how could you redistribute it so everyone has the exact same 'fair share'?
The mean is a single number that describes the 'center' of a data set. Think of it as the fair share. If you took all the values in a group and spread them out equally, the amount everyone gets is the mean. In mathematics, we call this a measure of center. To find it, you simply combine everything you have (the sum) and then divide it equally among the members of the group (the count).
Three friends have different numbers of stickers: , , and . Let's find the mean.
1. Add the values together: . 2. Count how many values there are: There are friends. 3. Divide the sum by the count: .
The mean is stickers.
Quick Check
If you are finding the mean of 10 different numbers, what number do you divide the total sum by?
Answer
You divide by 10.
To be a math pro, you can use a formula to represent the mean. If we let represent our values and represent how many values we have, the formula looks like this:
This works for any size of data! Whether you are averaging test scores or temperature readings, the process never changes: Sum then Divide.
A player scores the following points in four games: and .
1. Find the sum: . 2. Identify the count: There were games. 3. Calculate the mean: .
The player averaged points per game.
Quick Check
True or False: The mean must always be one of the numbers in your original data set.
Answer
False
The mean is very sensitive. If you add a new number that is much higher than the rest, it pulls the mean up. If you add a number that is much lower, it pulls the mean down. Imagine a group of 6th graders with a mean height of feet. If a professional basketball player who is feet tall joins the group, the 'fair share' height for everyone would increase significantly!
You have two test scores: and . Your current mean is . If you miss the third test and get a , what happens?
1. New Sum: . 2. New Count: tests. 3. New Mean: .
Adding a single low value (an outlier) dropped the mean from a perfect to a !
What is the mean of the data set: ?
If the mean of 5 numbers is 10, what is the sum of those 5 numbers?
Adding a very small number to a data set will usually decrease the mean.
Review Tomorrow
Tomorrow morning, try to explain to a family member why a single zero on a homework assignment can change your grade so much using the word 'Mean'.
Practice Activity
Find the 'Mean Age' of the people in your home. Add up everyone's age and divide by the number of people!