In this lesson, students find and interpret the mean of a distribution (MP2) as the amount each member of the group would get if everything is distributed equally. This is sometimes called the “leveling out” or the “fair share” interpretation of the mean. For a quantity that cannot actually be redistributed, like the weights of the dogs in a group, this interpretation translates into a thought experiment.
Suppose all of the dogs in a group had different weights and their combined weight was 200 pounds. The mean would be the weight of the dogs if all the dogs were replaced with the same number of identical dogs and the total weight was still 200 pounds.
Here students do not yet make an explicit connection between the mean and the idea of “typical,” or between the mean and the center of a distribution. These connections will be made in upcoming lessons.
- Comprehend the words “mean” and “average” as a measure of center that summarizes the data using a single number.
- Explain (using words and other representations) how to calculate the mean for a numerical data set.
- Interpret diagrams that represent finding the mean as a process of leveling out the data to find a “fair share.”
Let’s explore the mean of a data set and what it tells us.
- I can explain how the mean for a data set represents a “fair share.”
- I can find the mean for a numerical data set.
The average is another name for the mean of a data set.
For the data set 3, 5, 6, 8, 11, 12, the average is 7.5.
\(45 \div 6 = 7.5\)
The mean is one way to measure the center of a data set. We can think of it as a balance point. For example, for the data set 7, 9, 12, 13, 14, the mean is 11.
To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are. \(7+9+12+13+14=55\) and \(55 \div 5 = 11\).