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6.04 Pie charts, bar charts and stacked area graphs

Lesson

In today's information rich community it is important to get ideas across in an engaging and efficient form. You have probably come across many infographics in advertisements, magazines and presentations. An infographic is a collection of imagery, charts, and minimal text that strives to give an appealing and easy-to-understand overview of a topic.  Below is an infographic about space travel, specifically to the Moon, the information is represented in many different ways.

Infographic on visiting the Moon

To read infographics effectively you need skills in interpreting many different types of graphs. In this lesson we will look at interpreting a few familiar and unfamiliar charts that are often used.

Pie charts

A pie chart (pie graph or sector graph) is a special chart that uses a circle divided into slices(sectors) to show relative sizes of data. This chart is useful to display and compare parts of data that make up a whole, such as proportion of voters voting for particular political parties.

Reading a pie chart

There are $360^\circ$360° in a circle. Using this fact we can:

  • Find the angle, ($\theta$θ), for segments knowing fraction of the whole the segment represents:

$\theta=\text{Fraction of group in sector}\times360^\circ$θ=Fraction of group in sector×360°

  • Find the number a segment represents:

$\text{Number in a sector}=\frac{\theta}{360}\times\text{Number in whole group}$Number in a sector=θ360×Number in whole group

Practice question

Question 1

The sector graph represents the number of people taking leave from work at a particular company.

  1. If $5$5 people took leave in January, how many degrees represent $1$1 person?

  2. How many people took leave in November?

  3. How many people took leave between the beginning of November and the end of March?

  4. What percentage of the people took leave in December?

    Give your answer as a percentage, rounding to two decimal places.

Segmented bar charts

A segmented bar chart is a graph where the bar represents the whole data set and the bar is divided into several segments to represent the proportional size of each category. It is very similar to a pie chart but with a bar replacing the circle.

Practice question

Question 2

The divided bar graph below shows the popularity of certain types of restaurants in Valentina's home town.

  1. Which restaurant is the most popular?

    Mexican restaurant.

    A

    Italian restaurant.

    B

    Thai restaurant.

    C

    French restaurant.

    D
  2. Do more people go to French restaurants or to Thai restaurants?

    French restaurants

    A

    Thai restaurants

    B
  3. Which two restaurants are visited by the same number of people?

    Mexican and Indian

    A

    Indian and Thai

    B

    Thai and Italian

    C

    Indian and French

    D
  4. If $24$24 people went to an Indian restaurant, approximately how many went to a Mexican restaurant?

    $0$0

    A

    $24$24

    B

    $48$48

    C

    $96$96

    D

Grouped bar charts

Grouped bar charts are useful when comparing two related data sets on the same graph.

Practice question

Question 3

Study the bar graph below, which shows the changes in tourism rates in different cities during 2011 and 2012 , then answer the following questions.

  1. What is the difference between Shanghai's percentage of tourism over the 2 years?

    $25%$25%

    A

    $10%$10%

    B

    $20%$20%

    C

    $15%$15%

    D
  2. Which city had the greatest difference in percentages of tourism over 2011 and 2012?

    London

    A

    Tokyo

    B

    Rome

    C

    New York

    D
  3. Which city had the smallest difference in minimum and maximum percentages of tourism over 2011 and 2012?

    Singapore

    A

    Istanbul

    B

    Dubai

    C

    Paris

    D
  4. What is the difference between the minimum and maximum percentages of tourism of all the cities in the graph over the 2 years.

    $55%$55%

    A

    $65%$65%

    B

    $40%$40%

    C

    $60%$60%

    D

Stacked area graphs

Stacked area graphs are similar to line graphs in that they both display data that changes over time. However, while a line graph shows how one variable changes over time (e.g. a product's sales figures from a particular shop), a stacked area graph is used to show changes in several variables that make up the total in the data being graphed (e.g. total sales figures across several stores in a chain). A stacked area chart shows how much each part contributes to the whole amount. 

The area between axes and lines are commonly emphasised with different colours or patterns.  

For example, the area chart below displays the total revenue made by a business across three products. The difference between the lines indicates the amount of revenue made by each product. For example, in the fourth month, Product B made $\$3000$$3000 ($\$9000-\$6000$$9000$6000 ).

Watch out!

Don't just look at the vertical-axis to find a value at a particular point in time. You need to calculate the difference between the upper and lower lines to find the value of the variable. 

 

Worked example

Example 1

The revenues generated in thousands for a company from their four major products are shown in the area chart above.

(a) What was the monthly revenue generated by Product A in April?

Think: For the product at the bottom of the graph we need to just read the value of the line in April.

Do: In April, the line for Product A sits at $100$100. Hence, Product A produced $\$100000$$100000 revenue in April.

 

(b) What was the monthly revenue generated by Product C in May?

Think: We need to find the difference between the upper and lower lines for Product C in May.

Do: The top line for Product C sits at $450$450 and the bottom line sits on $300$300. As the difference is $150$150, Product C generated $\$150000$$150000 revenue in May.


(c) What percentage of the revenue in May was made by product C?

Think: We need to calculate the fraction of the revenue that Product C generated out of the total revenue in May and write this as a percentage.

Do: From part b) we have that Product C generated $\$150000$$150000 in revenue. Reading the top of the graph will give us the total revenue across the $4$4 products, hence, the total revenue in May is $\$550000$$550000.

$\text{Percentage revenue Product C in May}$Percentage revenue Product C in May $=$= $\frac{\text{Revenue for Product C}}{\text{Total revenue}}\times100%$Revenue for Product CTotal revenue×100%
  $=$= $\frac{150000}{550000}\times100%$150000550000×100%
  $\approx$ $27.3%$27.3%


Practice question

Question 4

The revenue generated in a company from their three major products are shown in the area chart to the right.

  1. What is the revenue generated by Product C in the first month?

  2. What is the maximum revenue generated by Product A?

  3. What is the difference between the revenue generated in month 4 and the revenue generated in month 5 by Product B?

  4. What is the total revenue generated by Product C during the 7 months?

  5. How much did the revenue generated by Product C exceed that of Product A in the 7th month?

Outcomes

1.3.1.1

interpret information presented in graphs, such as step graphs, column graphs, pie graphs, picture graphs, conversion graphs of calories ↔ kilojoules, line graphs using units of energy to describe consumption of electricity, including kilowatt hours

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