Finding the Average
Learn how to find the average of a set of numbers
1. The Big Idea: Evening Out
What is Average?
Average is what each value would be if we evened out all the values to be equal.
Example: Four Towers of Cubes
Four towers are built using different numbers of cubes: 3, 7, 6, and 4 cubes.
Think: If we move some cubes so that all four towers have the same height, how many cubes will each tower have?
After Evening Out
When we redistribute the cubes equally, each tower has 5 cubes!
The average number of cubes in each tower is 5.
2. The Formula
The Average Formula
Average = Total ÷ Number of items
Example: Connie's Quiz Scores
Connie took part in 4 quizzes. Her scores were: 24, 30, 12, and 20. What was her average score?
Step 1: Find the total score
Total = 24 + 30 + 12 + 20 = 86
Step 2: Count the number of quizzes
Number of quizzes = 4
Step 3: Calculate the average
Average = 86 ÷ 4 = 21.5
Connie's average score was 21.5.
3. Averages Can Be Decimals
Important!
The average can be a decimal, even when all the original values are whole numbers.
Example: Mass of 4 Children
The masses of 4 children are: 38 kg, 40 kg, 37 kg, and 42 kg. What is their average mass?
Total mass = 38 + 40 + 37 + 42 = 157 kg
Average mass = 157 ÷ 4 = 39.25 kg
Note: The average mass is 39.25 kg. This doesn't mean any child actually has a mass of 39.25 kg! It just shows the "typical" or "central" value.
4. Reading from Bar Graphs
Sometimes data is given in a bar graph. Read the values from the graph, then calculate the average.
Example: Samad's Books
The graph shows the number of books Samad read from September to December. What was the average number of books Samad read per month?
Step 1: Read values from graph: 6, 11, 10, 13
Step 2: Total = 6 + 11 + 10 + 13 = 40 books
Step 3: Average = 40 ÷ 4 = 10 books per month
Samad read an average of 10 books a month from September to December.
Example: Peter's Savings
The bar graph shows the amount of money Peter saves each month from January to May. What is his average savings per month?
Total savings = $60 + $90 + $80 + $75 + $50 = $355
Number of months = 5
Average = $355 ÷ 5 = $71
5. More Examples
Example: Three Towers
Three towers have 8, 7, and 6 cubes. What is the average number of cubes in a tower?
Total = 8 + 7 + 6 = 21 cubes. Average = 21 ÷ 3 = 7 cubes
Example: Watermelons in Crates
The total number of watermelons in 3 crates is 69. What is the average number of watermelons in each crate?
Total = 69 watermelons
Number of crates = 3
Average = 69 ÷ 3 = 23 watermelons per crate
Remember: Each crate doesn't need to have exactly 23 watermelons! One might have 20, another 25, and another 24. The average is just 23.
Key Points to Remember
- ✓Average = Total ÷ Number of items
- ✓Average is like "evening out" all values to be equal
- ✓Average can be a decimal (like 21.5 or 39.25)
- ✓Individual values don't need to equal the average
- ✓Always show your working: Total = ..., Average = Total ÷ Number = ...