Slide the blue points on the slider to move the data points on the number line below. Notice how the mean changes.

- Can you make the mean the same value as one (or more) of the data points? How many ways? What do you notice?
- Can you make more than one data set with a mean of 4?
- Will the mean ever be outside of the data set?
- Set up the points to 4,\,6 and 11. How far is each value from the mean? Use negative values for below the mean and positive values for above the mean. What is the sum of these values?

The **mean** is the balance point of a data set. This means that the sum of the distances from the mean of all of the points below the mean is equal to the sum of the distances from the mean of all of the points above the mean.

To find the balance point, when it is not given, points can be moved one-by-one towards the middle.

If the balance point is located between two values, we can find the halfway point between those values by averaging the numbers.

Adding or removing a data point might throw off the balance of the data set resulting in a new balance point.

A classroom recorded the number of pets for each student. The results for the class are represented in the given line plot.

a

What was the total number of pets for the entire class?

Worked Solution

b

What is the mean number of pets per student?

Worked Solution

During a fitness challenge, Alex recorded the number of push-ups completed each day. The table shows the number of push-ups Alex did.

Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

Push-ups | 15 | 20 | 15 | 10 | 15 | 20 | 10 | 15 | 20 | 20 |

a

Create a line plot of the data.

Worked Solution

b

What was the total number of push-ups completed?

Worked Solution

c

What is the balance point of push-ups completed each day?

Worked Solution

Use the given line plot to identify the mean of a group of friends shoe sizes.

Worked Solution

Idea summary

The **mean** is the balance point of a data set and is best when there are not any values which are far away from the rest.

To find the balance point from a line plot we alternate moving each point on the far left side and far right side one unit closer to the center of the line plot. Eventually, all the points should be at balance point, which is the mean of the data set.

The points located to the left of the balance point are the same distance away from the balance point as the points located on the right side.