9.01 Calculate the mean

Lesson

Practice

Ideas

The mean

The mean

The mean of a data set is an average of all the data values in the set. Let's look at an example.

Three friends are planning a trip to Alice Springs. They plan to fly there, and discover that the airline imposes a weight limit on their luggage of 20\text{ kg} per person. On the night before the flight they weigh their luggage and find that their luggage weights form this data set: 17,\,18,\,22

One of them has packed too much. They decide to share their luggage around so that they all carry the same amount. How much does each person carry now? Thinking about it mathematically, we are sharing the total luggage equally among three groups. We can represent that as an expression: \dfrac{17+18+22}{3}=\dfrac{57}{3}=19

Each person carries 19\text{ kg}. This amount is the mean of the data set.

To calculate the mean, use the formula:

Mean

=\dfrac{\text{sum of all data values}}{\text{number of data values}}

Examples

Example 1

Find the mean of this data set:4,\,7,\,1,\,2,\,3

Worked Solution

Create a strategy

Add the 5 data values together and divide by number of data values.

Apply the idea

\displaystyle \text{mean}	\displaystyle =	\displaystyle (4+7+1+2+3) \div 5	Add all the data values
	\displaystyle =	\displaystyle 17 \div 5	Divide the sum of the data values by the number of data values in the set
	\displaystyle =	\displaystyle 3.4	Evaluate the division

Reflect and check

Even though all the numbers in the data set are whole numbers, the mean is a decimal. If the data set was produced from a survey question "How many siblings do you have?", we would say the mean number of siblings was 3.4, even though it isn't possible to have 0.4 siblings. The mean is a way to summarize data - it is not part of the data set itself.

Idea summary

The mean of a data set is the average of all the data values in the set.