Lesson 7: Calculating the Mean. Pie Graph. Bar Graph
Lesson 7: Calculating the Mean. Pie Graph. Bar Graph
Find the mean, and read and make pie and bar graphs.
In this lesson you will learn what a mean is.
You will discover how the mean is related to the average.
For example, given a set of numbers: 2, 5, 7, 7, 8 the mean is calculated by first finding the sum of all numbers and dividing the sum by how many numbers there are in a set: (2 + 5 + 7 + 7 + 8)/ 5.
The mean is often used in research, academics and in sports.
The lesson will also teach you how and when to use pie graphs (charts). You often see these graphs used by media to show the relationships between various quantities ( for example, during the elections, bar or pie graphs are used to show the ratings of the candidates.
You will learn how to use bar graphs when representing the relationships between quantities that are not dependent on each other.
Key ideas: Calculating the Mean. Pie Graph. Bar Graph
The mean (average) is the sum of the values divided by how many values there are. The median is the middle value when the data is in order, and the mode is the most common value.
A bar graph compares amounts in categories. A pie graph (circle graph) shows parts of a whole: each part’s angle = (part ÷ total) × 360°.
Worked examples
Example 1
Find the mean of 12, 15, 9, 20 and 14.
- Sum: 70. Count: 5.
- Mean = 70 ÷ 5 = 14
Example 2
Sam scored 78, 85 and 90 on three tests. What must he score on the fourth test to have a mean of 85?
- A mean of 85 over 4 tests needs a total of 4 × 85 = 340.
- 340 − (78 + 85 + 90) = 87
Example 3
In a class of 30, 12 students chose soccer. What angle does soccer get in a pie graph?
- 12 ÷ 30 = 0.4 = 40%.
- 0.4 × 360° = 144°
Common mistakes
- Dividing by the wrong count when finding the mean.
- Finding the median without putting the data in order.
- Pie graph sections that do not add to 360° (or 100%).
Questions students ask
When is a pie graph better than a bar graph?
When you want to show parts of one whole. Bar graphs are better for comparing separate amounts.
Grade 8 Mean and Graphs Quiz
Check your understanding
Try the quiz for this lesson. You’ll see right away if each answer is correct.