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7.04 Interpret other charts and 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 travel to the moon containing information that 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

 

Bar graphs

A bar graph always presents a categorical data set. There is one column per category, and the height of each column is the size of that category. There is usually a small gap between each column. 

Both axes should be labelled to provide additional information about the data and tell us what type of values we have.

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

Outcomes

1.4.1

interpret information presented in graphs, such as: conversion graphs, line graphs, step graphs, column graphs and picture graphs

1.4.3

discuss and interpret graphs found in the media and in factual texts

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