About Statistics

Book A

TITLE Book Name:

About Statistics Book A: Starting with Statistics 600A 978-1-86968-478-5 2008

Book Code: ISBN 13: Published:

AUTHOR John Thompson

ACKNOWLEDGEMENTS The publisher wishes to acknowledge the work of the following people: Design: Editor:

Glen Honeybone Murray Quartly

PUBLISHER User Friendly Resources New Zealand PO Box 1820 Christchurch Tel: 0508-500-393 Fax: 0508-500-399

Australia PO Box 914 Mascot NSW 2020 Tel: 1800-553-890 Fax: 1800-553-891

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WEBSITE www.userfr.com

E-MAIL info@userfr.com

COPYING NOTICE This is a photocopiable book and permission is given to schools or teachers who buy this resource to make photocopies or transparencies of all pages. The copies must be for internal school use only, and may not be given or sold to other educational institutions or teachers from other institutions.

COPYRIGHT User Friendly Resources, 2008.

User Friendly Resources specialises in publishing educational resources for teachers and students across a wide range of curriculum areas, at both primary and secondary levels. If you wish to know more about our resources, or if you think your resource ideas have publishing potential, please contact us at the above address.

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About Statistics

Book A

Contents STARTING WITH STATISTICS

To the Teacher

4

Activity 1: Pie Graphs Activity Guidelines for Teachers Activity 1A: Constructing Pie Graphs Activity 1B: Creating a Table Activity 1C: Interpreting a Pie Graph Activity 1D: Review Questions Self-Assessment Answers

5 6-9 10 11 12-13 14 15

Activity 2: Dot Plots Activity Guidelines for Teachers Activity 2A: What Are Dot Plots? Activity 2B: Drawing and Reading Dot Plots Activity 2C: More Dot Plot Practice Activity 2D: Review Questions Self-Assessment Answers

16 17-18 19 20 21 22 23-24

Activity 3: Stem-and-Leaf Plots Activity Guidelines for Teachers Activity 3A: What Are Stem-and-Leaf Plots? Activity 3B: Drawing and Reading Stem-and-Leaf Plots Activity 3C: More Work with Stem-and-Leaf Plots Activity 3D: Review Questions Self-Assessment Answers

25 26-27 28 29 30 31 32

Activity 4: Time-Series Graphs Activity Guidelines for Teachers Activity 4A: What Are Time-Series Graphs? Activity 4B: Graphing Population Growth Activity 4C: Graphing Crime Rates Activity 4D: More Practice Activity 4E: Review Questions Activity 4F: Statistical Investigation Self-Assessment Answers

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33 34-36 37 38 39 40 41-42 43 44-45

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About Statistics

Book A

To the Teacher STARTING WITH STATISTICS It is not always easy for students to analyse statistical data and come to conclusions that are consistent with the information provided. This About Statistics series provides teachers with an accessible resource for guiding students through some of the more difficult steps. The material introduces the basic techniques necessary to carry out statistical analysis and investigation. The data in most of the activities is based on real life situations. It has been collected from newspapers and similar sources. Students will also be able to find data from libraries, or on the internet. Sources include Yearbooks and other statistical publications. The activities in the About Statistics series involve students in problem solving and cater to a range of learning styles including cooperative group activities. The activities can also be adapted to provide a programme of independent learning if needed. The study of statistics particularly lends itself to the use of software. As well as assisting students in what have historically been seen as tedious computing tasks, software also has an important role in allowing students to experiment with data. The software and hardware needed is often quite minimal. For most purposes a spreadsheet running on any computer will suffice. Also, data files allow students to investigate real-life data with all its complexity and ambiguity. The major pitfall to avoid with computers is students producing excessive numbers of printed graphs for their data without accompanying interpretations!

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About Statistics

Book A

1

Pie Graphs

F O C U S

Introduction

Creating pie graphs

This activity involves students in the construction, use and interpretation of pie graphs. It is necessary for the students to firstly review skills, such as drawing angles with a protractor and working with proportions, fractions and percentages.

Displaying survey results in graphical form Interpreting graphs

STARTING WITH STATISTICS

They then learn to construct pie graphs from data arranged in categories, and to use pie graphs in appropriate contexts. Emphasis is also placed on interpreting the information represented in pie graphs.

Teaching Ideas •

Ensure students can draw angles using a protractor.

•

Revise understandings of proportions.

•

Revise expressing a fraction as a percentage.

•

Examine examples of pie charts found in the media.

•

Discuss the advantages and disadvantages of using pie graphs.

•

Discuss what type of data can be represented by a pie chart.

Reinforcement

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•

Exploded pie charts and why they are used.

•

The misuse of pie charts.

•

The relative merits of using numbers or percentages in pie graphs.

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About Statistics

1A F O C U S Creating pie graphs Displaying survey results in graphical form Interpreting graphs

Book A

Constructing Pie Graphs STARTING WITH STATISTICS

What you need to know In constructing pie graphs there are a number of steps to be followed. 1. Firstly, make sure that there are not too many categories for your data. Pie graphs can become very cluttered and hard to read if there are more than 6 categories. 2. Next, you need to find out how many data items there will be in each category. Put the data into a frequency table like the one in the example below. 3. Work out what fraction of the circle will be used for each category. 4. Then, when you have all this information, you draw and label the pie graph. Note: Often each sector in a pie graph is labelled with a percentage as well as its category name. The percentage shows the number of items in that category as a percentage of the total number of items. Example Question The 25 students in Room 6 were asked to say which type of video they liked the best from the following list:

• • • •

Music Sport Comedy Documentary

Here are their results: Number

Angle

Percentage (Nearest Whole number)

Music

5

72o

20%

Sport

10

114o

40%

Comedy

4

57.6o

16%

Documentary

6

86.4o

24%

Totals

25

360o

100%

Category

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About Statistics

1A F O C U S Creating pie graphs Displaying survey results in graphical form Interpreting graphs

Book A

Constructing Pie Graphs STARTING WITH STATISTICS

The rule for calculating the angle for each category is: angle = 360˚ x (number in category) ÷ (total number for all categories) Calculations

Music Sport Comedy Documentary

360˚ x 5 ÷ 25 360˚ x 10 ÷ 25 360˚ x 4 ÷ 25 360˚ x 6 ÷ 25 Total

= = = = =

72˚ 144˚ 57.6˚ 86.4˚ 360o

The rule for calculating the percentage for each category is:

Music Sport Comedy Documentary

percentage = (number in category) ÷ (total number for all categories) x 100% 5 ÷ 25 x 100 % = 20% 10 ÷ 25 x 100% = 40% 4 ÷ 25 x 100% = 16% 6 ÷ 25 x 100% = 24% Total = 100%

Drawing Pie Graphs – Procedure 1. Draw a circle of the size required.

2. Mark a horizontal radius on the right half of the circle.

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About Statistics

1A F O C U S

Book A

Constructing Pie Graphs STARTING WITH STATISTICS 3. Use a protractor and measure the angles, stepping around the circle, starting at the horizontal radius.

Creating pie graphs Displaying survey results in graphical form Interpreting graphs

continue moving around the circle. 72o

Note: To ensure you are correct, total all the category angles. They should add to 360o.

Now we have all the information needed to draw the pie graph. Here it is.

Video Choices

Music

20%

Documentary

24%

Comedy Sport

40%

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16%

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About Statistics

1A F O C U S Creating pie graphs Displaying survey results in graphical form Interpreting graphs

Book A

Constructing Pie Graphs STARTING WITH STATISTICS

What you need to do 1. Complete the following table, and then draw the pie graph that goes with it. A group of 18 students were asked to say which sport they most enjoyed watching on television. They had a list of 6 sports to choose from. The results of this survey are shown in the table. Sport

Number

Cricket

3

Rugby

4

Netball

4

Basketball

2

Soccer

4

Tennis

1

Angle o

Percentage o

360 x 3 ÷ 18 = 60

3 ÷ 18 x 100 = 17%

Totals

2. Use the information below to draw a pie graph on your own paper. On Tuesday afternoons students in Room 8 choose from one of five different options. Their choices are: Art, Music, French, Japanese and Drama. The number of students choosing each subject are shown below. Art Music French Japanese Drama

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6 4 2 2 10

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About Statistics

1B F O C U S Creating pie graphs Displaying survey results in graphical form Interpreting graphs

Book A

Creating a Table STARTING WITH STATISTICS

What you need to do 1. A student made the following list of the types of cars driven by the teachers at her school. Teacher

Car

Miss Lee

Toyota Corolla

Mr Jackson

Honda Civic

Krs Kingi

Toyota Corona

Mr Clarke

Mazda Familia

Ms Lucas

Toyota Celica

Miss Patel

Nissan Sunny

Mrs Smythe

Nissan Sentra

Mr Change

Triumph 2500

Mrs Clarke

Toyota MR2

Dr Sturmer

Honda Prelude

Ms Browne

Honda Civic

Mrs Tamati

Toyota Corolla

Make a table, and then draw a pie graph on your own paper to display information about the make of car driven by the teachers. Your categories should be based on the make (eg. Toyota) and not the model (eg. Corolla) for each car. 2. Someone looks at the data above and your pie graph and says it would have been better to use a picture graph or a bar graph for this data. Write a sentence or two explaining why you agree (or disagree) with this.

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About Statistics

1C F O C U S Creating pie graphs Displaying survey results in graphical form Interpreting graphs

Book A

Interpreting a Pie Graph STARTING WITH STATISTICS

What do you need to do The purpose of this exercise is to process data and interpret information from pie graphs. 1. The following pie graph was made from a survey of 24 Toyota Corollas in a car yard. By measuring the angles in the graph complete the table below.

Toyota Corollas Yellow Red Blue

White

Colour

Angle

Number

Red White Blue Yellow

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About Statistics

1D F O C U S Creating pie graphs Displaying survey results in graphical form

Book A

Review Questions STARTING WITH STATISTICS

The purpose of these exercises is to draw, process and interpret information from pie graphs. A. In a survey of fish caught by holiday makers, a student researcher recorded the following information about each person and the fish they had in their bucket.

Interpreting graphs Age of fisher

Fish caught

13

5 sprats and 2 piper

12

4 parore

35

5 parore and 3 sprats

42

7 sprats

27

5 piper and 2 sprats

9

1 eel and 1 gurnard

65

2 gurnard and 1 snapper

37

3 sprats

41

1 eel

Put this data into categories so that it could be used in a pie graph to display information about the types of fish that are being caught. B. Match each set of data with the type of graph that would be best used to display it. Give a reason why you have chosen each graph for each example. Types of graph:

Bar

Pie

Data:

Types of footwear worn by students in Room 6.

Temperature in Room 6 at noon each day during the week.

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About Statistics

1D F O C U S

Book A

Review Questions STARTING WITH STATISTICS

C. Complete the table below by working out the angle and percentage for each category of data.

Creating pie graphs Displaying survey results in graphical form Interpreting graphs

Data for the hair colour of children in Room 8 Category

Number

Red

2

Blue

1

Brown

15

Black

8

Blonde

4

Angle

Percentage

D. Draw a pie graph using the table in question C.

E. What colour cars are twice as likely to be caught speeding as the blue ones? Use the pie graph to work out your answer.

Speeding Cars White

Black Blue

Green Red

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About Statistics

1

Book A

Self-Assessment STARTING WITH STATISTICS Use the confidence level scale on the right to assess how confident you feel about each of the activity questions. Tick on the scale for each concept.

CONCEPT

Confidence level scale 1 = I donâ€™t understand it at all. 2 = I would find it difficult. 3 = I could do it, but not easily. 4 = I know how to do this, but would like more practice. 5 = Too easy, give me a challenge!

EXAMPLE

I know how to group data into categories.

Draw a table showing what categories this data would go into.

I know what type of data can be used in a pie graph.

CONFIDENCE LEVEL 1

2

3

4

5

What type of graph would be best for the information from these tables.

1

2

3

4

5

I know how to calculate the angle for each category of data in a pie graph.

Work out the angle and percentage for each category of data in this table.

1

2

3

4

5

I know how to draw an accurate pie graph once I have worked out the angles for each category.

Draw a pie graph using this information.

1

2

3

4

5

Make mathematical statements about information shown in a pie graph.

Use this pie graph to work out which colour car was most often caught speeding.

1

2

3

4

5

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About Statistics

Book A

1

Answers STARTING WITH STATISTICS

Activity 1A 1.

Sport Cricket Rugby Netball Basketball Soccer Tennis Totals

Number 3 4 4 2 4 1 18

Angle 60˚ 80˚ 80˚ 40˚ 80˚ 20˚ 360˚

Percentage 17% 22% 22% 11% 22% 6% 100%

2.

Room 8 Options

Art 25%

Drama 42%

Music 17%

Japanese 8%

Activity 1B 1.

Make Honda Mazda Nissan Toyota Triumph

French 8%

Activity 1C Number 3 1 2 5 1

1.

Teachers’ Cars Triumph 8%

Honda 25% Toyota 42%

2. A bar graph can be easier to read and gives the category totals directly.

Colour Red White Blue Yellow

Angle 90˚ 180˚ 60˚ 30˚

No. 6 12 4 2

Mazda 8%

Nissan 17%

Review Questions 1D A.

Fish Sprat Piper Parore Eel Gurnard Snapper

Number 20 7 9 2 3 1

Review questions C. Category Number Red 2 Blue 1 Brown 15 Black 8 Blonde 4 Totals 30

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B. Footwear - pie graph. The footwear forms categories which are easily displayed as a pie graph. Temperature - bar graph. The bars display temperature as a rise or fall.

Angle 24˚ 12˚ 180˚ 96˚ 48˚ 360˚

Percentage 7% 3% 50% 27% 13% 100%

D.

Hair Colour of Room 8 Children Black 27%

Blonde 13%

E. Red cars

Red 7% Blue 3%

Brown 50%

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