Calculating the Mean

Lesson Plan - Get It!

Audio:

Working with numbers helps us figure out information in our lives.

In our opening example, you are trying to figure out what your average grade is for your math course after taking 5 math tests. Knowing this information will tell you how well you did in your course.

In order to understand how to find the mean in a set of numbers, you first need to define some math vocabulary. On a piece of paper, write the definitions of the following words. You can look them up in an online dictionary like merriam-webster.com:

1. data
2. mean
3. operations
4. sum

When figuring out the mean of a set of numbers, you need to follow a few steps, and sometimes use more than one operation.

One tool that can help you work with more than one operation is known as PEMDAS. Each letter in PEMDAS is the first letter of a mathematical operation. The order that the letters are in signifies the order in which you solve the operations.

Let’s break PEMDAS down and see what each letter stands for:

• P = Parentheses
• E = Exponents
• M = Multiplication
• D = Division
• A = Addition
• S = Subtraction

If you are working on a math problem that requires more than one operation, you will solve the problem by completing what is in parentheses first, then solve any exponents, solve any multiplication in the problem, solve any division, solve any addition, and, finally, solve any subtraction in the problem.

That is the order in which you work with different operations in one math problem. Note: You will not necessarily use all these operations to solve a math problem for the mean. Also, it is very rare to have a math problem that contains all of the operations in it.

Now that you are equipped with the PEMDAS tool, you are ready to begin your adventure of finding the mean.

Let’s look back at the problem at the beginning of our lesson. We know the following information:

• You have taken 5 tests in your math course.
• You received the following grades on those five tests: 87, 95, 76, 85, and 88.

What we do not know is the average grade you received for your math course.

Set up your problem with numbers instead of words.

On a sheet of paper, write an addition problem for the five test grades that you have received. Your problem should look like this:

(87 + 95 + 76 + 85 + 88) Make sure you include the set of parentheses around the problem.

You can see each of your test grades in this problem. Now, go through the steps!

Step 1 is to add all of the data (numbers). We have set up our problem to do that. However, we cannot work the problem out just yet.

Step 2 is to divide our sum by the number of grades we are adding together. We have 5 test grades, so we will be dividing our sum by 5.

We need to put this information into our problem. When doing so, we are going to separate the addition part of the problem and the division part of the problem by a set of parentheses, so our problem now looks like this:

(87 + 95 + 76 + 85 + 88) ÷ 5 =

Now that we have completed the process of setting up our problem, we can start solving for our answer.

Remember PEMDAS? Do you remember what the P stands for? Exactly! The P stands for parentheses. So our first step in solving for our answer is to add the information that is in the set of parentheses.

What did you get for an answer? What is the sum of the numbers inside the parentheses?

Since we have completed solving the operation in the parentheses, we can get rid of the parentheses, and perform the division operation.

Your problem should look like this:

431 ÷ 5 =

After dividing 431 by 5, what did you get as an answer? Did you get 86.2%? If so, CONGRATULATIONS! Not only did you get the correct answer for this problem, but you ended up with a really good math grade! You can drop the .2 and write your answer as just 86%.

Now that you've done so well, continue on to the Got It? section to solve some more problems and teach someone else!