**High School Number Sense Lesson 21: Finding the Mean (Average) of a Set of Numbers**

The ability to find the arithmetic mean was tested

**9 times**this year--7 of the questions appeared in

**questions 11 - 17**, and 2 in the 40s. Most people with any math skills know how to find the average of a set of numbers. But I'm guessing you've never done it quite like this.

**Number Dojo Level: 78**

The

**arithmetic mean**is found by dividing the sum of a set of numbers by the number of terms in the set. It is different from the

**geometric mean**and the

**harmonic mean**, which we'll learn about later. The traditional way to find the average of numbers is:

- Add the numbers together.
- Count the numbers, and
- Divide the sum of the numbers by the count.

**The Quicker Way**

Let's say you are given a set of numbers that are relatively close to each other, such as 64, 61, 67, 62, and 66. To find their average, follow these steps:

- Pick an easy (round)
**target number**that will be close to the average. In this case,**60**. - Subtract the target number from each of the numbers, and add all the differences. Think: 4 + 1 + 7 + 2 + 6 =
**20**. - Find the average of these differences by dividing the sum by the count.
**20****÷ 5 = 4**. - Add this average back to the target number, and you have your average of the original numbers. 4 + 60 =
**64**.

**Example 1: The arithmetic mean of 29, 20, 27 and 28 is ___**

- Pick a target number:
**20**. - Subtract the target from each number, and add all the differences. Think: 9 + 0 + 7 + 8 =
**24**. - Find the average. 24 ÷ 4 =
**6**. - Add this average to the target. 6 + 20 =
**26**. This is your arithmetic mean.

**Example 2: The mean of 45, 48, 50, 46 and 41 is ___**

- Pick a target:
**40**. - Add the differences. Think: 5 + 8 + 10 + 6 + 1 =
**30**. - Find the average. 30 ÷ 5 =
**6**. - Add the average to the target. 6 + 40 =
**46**. This is your mean.

**Example 3: The average of 96, 97, 95, 96, 98, 96, 98, 99, and 98 is ___**

- Pick a target. Just for fun, let's pick
**95**, so you can see that it works as well. - Add the differences. Think: 1 + 2 + 0 + 1 + 3 + 1 + 3 + 4 + 3 =
**18**. - Find the average. 18 ÷ 9 =
**2**. - Add the average to the target. 2 + 95 =
**97**. This is your average.

**Example 4: The mean of 55, 56, 52, 54, and 52 is ___**

- Pick a target:
**50**. - Add the differences. Think: 5 + 6 + 2 + 4 + 2 =
**19**. - Find the average. 19 ÷ 5 =
**3.8**. (I used**DivDouble1st**and changed 19 ÷ 5 to**38 ÷ 10**). - Add the average to the target. 3.8 + 50 =
**53.8**. This is your mean.

**Example 5: The mean of 38, 41, 43, and 39 is ___**

- Pick a target. I'm going to pick
**40**this time to show you some negativity. - Add the differences. Think: (-2) + 1 + 3 + (-1) =
**1**. - Find the average. 1 ÷ 4 =
**1/4**or**.25**. - Add the average to the target. .25 + 40 =
**40.25**.

**Example 6 (Shaking it Up): The arithmetic mean of 24, 21, and ___ is 18**

- (This problem showed up on the State test this year). Since you are given the mean, multiply it by the count to find the sum of the numbers. 18 x 3 =
**54**. - Subtract the other two numbers to find the unknown third number. 54 - 24 - 21 =
**9**.

**Here's a free worksheet to help you practice FindMeanAvg:**

findmeanavg.pdf |

**Up Next for High School: AddSquareTrip (my personal favorite)**