Lesson 18: Average

New Concept

An average is a central value for a set of numbers, found by making groups equal. A line graph displays data as points connected by lines, often showing change over time.

What’s next

This is your introduction to these concepts. Next, you’ll tackle worked examples on calculating averages and interpreting data from line graphs to solve problems.

Property

To find the average of a set of numbers, we add the numbers to find the total and then divide the total by the number of numbers in the set to create equal groups. This is also called the mean.

Examples

Find the average of 25, 30, and 35 students: $\frac{25 + 30 + 35}{3} = \frac{90}{3} = 30$ students.
Find the average of the numbers 4, 9, and 11: $(4 + 9 + 11) \div 3 = 24 \div 3 = 8$.
Find the average of 20, 30, 40, and 50 dollars: $\frac{20 + 30 + 40 + 50}{4} = \frac{140}{4} = 35$ dollars.

Explanation

Think of 'average' as the 'fair share' number! Imagine you and your friends have different amounts of candy. To find the average, you first pool all the candy together into one giant pile (that's the 'adding' part). Then, you divide it all up evenly among everyone (that's the 'dividing' part). Now everyone has the same amount—the average!

Property

The number halfway between two numbers is the average of those two numbers.

Examples

• The number halfway between 27 and 81 is their average: $\frac{27 + 81}{2} = \frac{108}{2} = 54$.
• To find the midpoint on a number line between 28 and 82, you calculate their average: $\frac{28 + 82}{2} = \frac{110}{2} = 55$.
• What number is exactly halfway between 86 and 102? Simply find the average: $\frac{86 + 102}{2} = \frac{188}{2} = 94$.

Explanation

Ever tried to hang a picture exactly in the middle of a wall? Math gives you the perfect tool! Finding the point 'halfway between' two numbers is a secret mission, and the secret code is to just find their average. Add the two numbers together and divide by two to find that perfect center spot every single time.