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Statistics and probability

Course: Statistics and probability > Unit 3

Lesson 1: Measuring center in quantitative data
Math
Statistics and probability
Summarizing quantitative data
Measuring center in quantitative data
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Calculating the mean

Google Classroom
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:
Four names with pictures of identical cookies above them. Clair has five cookies above her name. Brook has three cookies above her name. Deandra has six cookies above her name. Lucy has two cookies above her name.
Imagine that the girls combined all of their cookies
Sixteen cookies in a pile with no particular order or organization.
and then each took the same number of cookies.
Four names with pictures of identical cookies above them. Clair has four cookies above her name. Brook has four cookies above her name. Deandra has four cookies above her name. Lucy has four cookies above her name.
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.
Four names with pictures of identical bananas above them. Bob has two bananas above his name. Bruno has two bananas above his name. Taz has five bananas above his name. Dimitri has three bananas above his name.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
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 {7,2,8,6,7}:
7+2+8+6+7=30Step 1305=6Step 2
The mean of this data set is 6.

Calculating the mean walkthrough

Let's find the mean of the data set {2,1,2,4,5,4} together.
Add up all of the data points.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

How many data points are in the data set?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Great! Now divide the total by the number of data points.
The mean of this data set is
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
.

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

Practice

Find the mean of the data set {5,23,8,12}.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Find the mean of the data set {2,7,5,4,6,3}.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Find the mean of the data set {4.5,5,3.5,2,2.5}.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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