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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.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
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 brace, 7, comma, 2, comma, 8, comma, 6, comma, 7, right brace:
7+2+8+6+7=30Step 1305=6Step 2\begin{aligned} 7 + 2+ 8 + 6 + 7&= \blueD{30} &\small{\gray{\text{Step 1}}} \\\\\\\\ \dfrac{\blueD{30}}{5} &= 6&\small{\gray{\text{Step 2}}}\end{aligned}
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.
Add up all of the data points.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

How many data points are in the data set?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
.

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

Practice

Find the mean of the data set left brace, 5, comma, 23, comma, 8, comma, 12, right brace.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Find the mean of the data set left brace, 2, comma, 7, comma, 5, comma, 4, comma, 6, comma, 3, right brace.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Find the mean of the data set left brace, 4, point, 5, comma, 5, comma, 3, point, 5, comma, 2, comma, 2, point, 5, right brace.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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