Students’ Integrated Maths Module for Bivariate Data 1 · [SIMM] Bivariate Data 1 3 Introduction...

Students’

Integrated Maths

Module

for

Bivariate Data 1

Author: Mark R. O’Brien

Editor: Mark R. O’Brien

OTRNet Publications

www.otrnet.com.au

Check our website for contact details.

Copyright © 2001 by OTRNet Publications, www.otrnet.com.au. All rights reserved. Nopart of this publication may be reproduced or transmitted in any form, or by any means,electronic or manual, including photocopying, scanning, recording, or by any informationstorage or retrieval system, without permission in writing from the publisher.

First published: November 2001First reprinted: January 2004Revised: January 2019

Design and Editing: Mark R. O’Brien Cover Design: Ali B Design

Ph: 0411 4301 09E-mail: [email protected]

National Library of AustraliaCataloguing-in-Publication data

For secondary studentsISBN 1 876800 25 9

3[SIMM] Bivariate Data 1

Introduction for students:

At the end of this module you should have increased your ability to;

C Plan what bivariate data to collect to answer questions (with other students)C Collect and record bivariate dataC Classify, sequence and tabulate bivariate dataC Graph bivariate data as line graphs and scatter graphsC Read bivariate data in tables and graphsC Comment on trends and patterns in bivariate dataC Sketch graphs to show the relationship between two quantitiesC Describe from a graph the relationship between two quantities

Table of Contents:

Activities:

A: Monitoring Plant Growth 4 Puzzle:

B: Tracking The Temperature 5 Australian Highways 25

C: Graphic Stories 6

D: Experimental Results 8 Applications:

E: Height Genetics 13 A: Predicting Water Storage 26

F: Getting To School 15 B: Temperature Relationships 29

C: High Marking 32

Student Recording 16 D:Temperature Predictions 34

E: Misleading Line Graphs 35

Notes 17 F: Newspaper Search: Bivariate Data 37

G: Project: Finding Relationships 38

Exercises:

1: Line Graphs 18 Student Reflection 39

2: Interpreting Graphical Trends 21

3: Scatter Graphs 22 Answers to Exercises 40

4: Travel Graphs 23

© OTRNet Publications: www.otrnet.com.au

4 [SIMM] Bivariate Data 1

Activity A:Materials required: Seeds, water, growing medium, graph paper

Monitoring Plant Growth

You will be planting seeds and monitoring the growth of theseedling over time by measuring its height each day.

Task 1: What two quantities (measurements) are involved inthis activity?

Because there are two quantities this is known as bivariate data. Bivariate datawhere time is one of the quantities, is also known as time series data.

Task 2: Plant out 4 seeds into the growing medium.

Task 3: Construct a table to record the height of the seedlings each day.

Task 4: Plot the height of your seedlings against time in a graph like the one set uphere. Connect up each days recording to form a line graph. You willneed to decide on and use a legend (key) to plot the growth of eachseedling on the same graph.



Activity B:

Tracking the Temperature

Task 1: Using the newspaper, television weather report, Internet orsome other source find out the maximum and minimumtemperatures each day for 14 days.

Task 2: Design a table for recording the date, the maximumtemperature and the minimum temperature over the 14 days.

Task 3: Record the location the temperatures are for, and the sourceof your data.

Task 4: Record your results for each of the 14 days in your table.

Task 5: Explain why this data is bivariate data.

Task 6: Explain why this is time series data.

Task 7: Keep your data for use in Application D.



Activity C:

Graphic Stories

This graph tells the story of James’ hunger during the day. “James is always starving when he wakes upin the morning so the first thing he does is eata big breakfast. He is then able to gothrough to lunchtime before once againeating heaps for lunch. He then grabs a biteto eat when he gets home from school to lasthim until he has a good sized dinner andthen he has a few snacks before bed time”.

Task 1: Write a story like the one above about how your hunger changes during the

day.

Task 2: Sketch a graph like the one above to show your hungerlevels during the day.

Task 3: Explain your graph to another member of your group.

Task 4: Sketch a graph to show Abbey’s hunger levels during the day by readingthe story of Abbey’s hunger below:

“ When Abbey wakes up (late) she is not very hungryso she skips breakfast and goes off to school. By thetime she gets there her hunger has increased so shegoes to the canteen for toast before the bell rings. Atrecess she goes to the canteen with her friends andgets more food, at lunchtime she does the same. After school she’s on the phone to her friends untilbed time so she doesn’t have time for dinner and justeats snacks constantly.”

Task 5: Compare your graph to another students’ and discusshow each of the graphs match the story. Make anyimprovements to your graph that you found throughyour discussion.



Task 6: Sketch a graph on axes likethose here, showing thenumber of people in theschool canteen during theday, from before school toafter school.

The graph here shows the noise levels in your classes during one school day.

Task 7: Write a story about what happened during each period of the day withreference to the noise levels.

Task 8: Draw sketch graphs for the following situations:

A: The popularity of a good song from when it is firstreleased until after it has been out for a while.

B: The temperature during a winters day.

C: The temperature during a summers day.

D: The speed a person runs at in a 100m sprint race.

E: The amount of soft drink in a can as you drink it.

F: The taste in a chewie from when you put it in your mouthuntil you get told to put it in the bin.

Task 9: Compare your graphs to another person in your group. Discuss where theyare similar and different.



Activity D: Materials required: graph paper

Experimental Results

A: Linear Data

A1: The data in this table represents a car travelling at 60km/h.

Time (h) 0 1 2 3 4 5 6 7 8

Distance (km) 0 60 120 180 240 300 360 420

Task 1: Plot these points on a graph of time against distance. Connect your valueswith a straight line.

Task 2: What is the missing distance value for the table?

This bivariate data can be modelled by what is known as a linear function. This type offunction models directly proportional quantities.

A2: The data in this table represents the results from an experiment where acandle is burnt.

Time (min) 0 10 20 30 40 50 60 70 80

Melted candle (mm) 0 5 8 13 20 27 28 35

Task 3: Plot these points on a graph of time against melted candle. Connect eachpair of values with a line.

These experimental results could best be modelled with a linear function.

Task 4: Use a ruler to draw a line of best fit on the values in your graph.

Task 5: Estimate the missing value in the table for melted candle.

Task 6: Give two reasons why the experimental results may not have exactlyfollowed this straight line.



B: Quadratic Data

B1: The data in this table gives the area of various squares.

Length of square (cm) 0 1 2 3 4 5 6 7 8

Area of square (cm2) 0 1 4 9 16 25 36 49

Task 7: Plot these points on a graph of length against area. Connect your valueswith a smooth curve.

Task 8: What is the missing area value for the table?

This bivariate data can be modelled by what is known as a quadratic function. Theshape of this graph is known as a parabola.

B2: The data in this table represents the results from an experiment wherea ball is dropped from a tall building.

Time (s) 0 1 2 3 4 5 6 7 8

Distance fallen (m) 0 5 28 39 83 117 195 244

Task 9: Plot these points on a graph of time against distance fallen. Connect yourvalues with a smooth curve that best fits the values you have.

Task 10: Estimate the missing value in the table for distance fallen.

These experimental results could best be modelled with a quadratic function.

Task 11: Give two reasons why the experimental results may not have exactlyfollowed the smooth curve (parabola).



C: Exponential Data

C1: The data in this table gives the number of cells in a growingorganism.

Time 0 1 2 3 4 5 6 7 8

Cells 1 2 4 8 16 32 64 128

Task 12: Plot these points on a graph of time against cells. Connect your values witha smooth curve.

Task 13: What is the missing number of cells for the table?

This bivariate data can be modelled by what is known as an exponential function.

C2: The data in this table shows the growth in the number of Internet usersin its first ten years.

Year 85 86 87 88 89 90 91 92 93 94 95 96

Users(millions)

0 0.1 0.3 0.4 0.5 0.6 1.0 1.4 2.3 3.9 7.8

Task 14: Plot these points on a graph of year against users. Connect your valueswith a smooth curve that best fits the values you have.

Task 15: Estimate the missing value in the table for users in 1996.

These experimental results could best be modelled with an exponential function.

Task 16: Give two reasons why Internet users may not have exactly followed thesmooth curve.



D: Reciprocal Data

D1: The data in this table gives the shares in a $1 million prize fordifferent amounts of people in a syndicate.

People 1 2 4 5 10 20 50 100

Prize share ($) 1,000,000 500, 000 250,000 200,000 100,000 50,000 20,000

Task 17: Plot these points on a graph of people against prize share. Connect yourvalues with a smooth curve.

Task 18: What is the missing value for the prize share with 100 people?

This bivariate data can be modelled by what is known as a reciprocal function. Thisfunction models inversely proportional quantities.

D2: The data in this table represents the results from anexperiment measuring the current flowing in circuits withdifferent resistance.

Resistance 1 2 3 4 5 6 7 8

Current 24 11.5 9 5 4.8 3.8 3.3

Task 19: Plot these points on a graph of resistance against current. Connect yourvalues with a smooth curve that best fits the values you have.

Task 20: Estimate the missing value in the table for current.

These experimental results could best be modelled with a hyperbolic function.

Task 21: Give two reasons why the experimental results may not have exactlyfollowed the smooth curve (hyperbola).



E: Periodic Data

E1: The data in this table gives the height of the tide at varioustimes of the day.

Time 8am 9am 10am 11am 12 1pm 2pm 3pm 4pm 5pm 6pm 7pm 8pm

Height (m) 2.0 2.5 2.7 2.5 2.0 1.5 1.3 1.5 2.0 2.5 2.7 2.5

Task 22: Plot these points on a graph of time against height. Connect your valueswith a smooth curve.

Task 23: What is the missing height value for the table?

This bivariate data can be modelled by what is known as a periodic function. This typeof function is used to model data that repeats itself.

E2: The data in this table represents the results from anexperiment where the height of a swing was measured overtime.

Time (s) 0 1 2 3 4 5 6 7 8

Height (m) 1.0 1.3 1.5 1.4 0.9 0.7 0.5 0.6

Task 24: Plot these points on a graph of time against distance fallen. Connect yourvalues with a smooth curve that best fits the values you have.

Task 25: Estimate the missing value in the table for distance fallen.

These experimental results could best be modelled with a periodic function.

Task 26: Give two reasons why the experimental results may not have exactlyfollowed the smooth curve (sine curve).



Activity E:Materials required: graph paper

Height Genetics

In this activity we are going to use a scatter graph to find out if there isa relationship between your height and your parents’ heights.

Task 1: What sort of relationship do you think there is betweenyour height and your parents?

Task 2: Do you think this is true for all people? Explain.

Task 3: Measure your height and record it here.

Task 4: What height is your same sex biological parent?

Task 5: Add your bivariate data to the class results.This should be as a pair of measurements; (your height, parent’s height).

Task 6: Draw up a set of axes for your scatter graph like the ones shown here:

You will need to check the class results to decide what values should go onthe scales. It is not necessary to start at zero.



Task 7: Complete the scatter graph by drawing a dot on the graph to representeach class member’s results.

Task 8: When you have completed your scatter graph describe any pattern yousee in the spread of dots.

Task 9: Compare your scatter graph to these examples, which is it most like?

Task 10: The labels under these scatter graphs describe the type of relationshipthe scatter graph shows. None - means there is no relationship between the two measurements.Positive - this means if one measurement is small, the other tends to be

small, if one is large, the other tends to be large.Negative - this means if one measurement is small, the other tends to be

large, if one is large, the other tends to be small.

What is the relationship between student height and parent height in yourclass?

Task 11: Explain what the relationship for your class means in terms ofa student’s height and the height of their parent.



Activity F:

Getting to School

The graph of bivariate datashown here is known as a travelgraph as it shows distancegraphed against time for a journey.

This graph represents Zarshua’sjourney to school each day.

It shows her walking to the bus stop,waiting for the bus and thentravelling on the bus to school.

Task 1: Describe how the graph relates to the parts of Zarshua’s trip, referring tothe letters A, B, C and D.

Task 2: Describe how a slow speed (walking) compares to a fast speed (the bus trip)on the graph.

Task 3: What does a flat section (B to C) mean in terms of speed?

Task 4: Sketch a new version of the graph to show the bus stopping three times forabout half a minute each time.

Task 5: Explain the changes you made to the graph.

Task 6: Sketch travel graphs for the following journeys:

A: Your journey to school.B: Amanda who rides to the bus stop then catches the bus.C: Cale who catches the bus outside his house.D: Matthew whose Mum drives him to school.E: Hayley who walks about 1km away from school to the bus stop

before catching the bus.



Student Recording:

Write at least two pieces of information about each of theseconcepts that you have explored in earlier lessons. Then try togive an example relating to each. Use diagrams where it helps.

bivariate data:

time series data:

line graph:

travel graph:

scatter graph:



Notes

Bivariate data

Bivariate data is data where there are two quantities or measurements for each piece ofinformation. These quantities are usually known as variables, hence the word bivariate,for two variables.

Line graphs

A line graph is used to represent some types of bivariate data. The most common usefor a line graph is where a quantity is measured over a period of time. This is alsoknown as Time series data. The line graph makes it easier to follow trends andpatterns in the data.

Travel graphs

This is the name given to a line graph which represents ajourney. It shows distance or speed against time. Examples ofthese were developed in Activity F.

Function graphs

For some bivariate data there is an underlying rule or function that can be used tomodel the data. Examples where this applied were shown in Activity D.

Scatter graphs

A scatter graph helps to find if there is a relationship between the two quantities thatmake up the bivariate data. Activity E involved you in looking for the relationshipbetween the height of a student and their parent’s height.



Exercise 1: Line Graphs

1. This table shows the rainfall in Cairns over one week.

Day Mon Tue Wed Thu Fri Sat Sun

Rainfall (mm) 22 28 10 35 28 21 7

Draw a line graph to represent this data.

2. This table shows the mean school attendance figures at a high school for one year.

Month Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Attendance (%) 95 94 91 89 89 85 84 90 ? 93 89

(a) Draw a line graph to represent this data.

(b) Comment on the trend that the graph shows.

(c) Use your graph to estimate the missing value for October.

3. Chart position of “Can We Fix It ” in the Top 40.

Week In 1 2 3 4 5 6 7 8 9 10 11 12

Position 25 16 10 5 2 1 1 3 7 15 26 39

You will need to think about the vertical scale to show this data effectively.

(a) Draw a line graph to represent this data.

(b) What did you need to do with the vertical scale to represent this data?

(c) Describe the trend in the data.



Source: Cancer Council of WA

4. This data shows petrol prices at two petrol stations.

Date 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

Price(c/L)

Gull 88.9 89.1 90.6 92.5 89.5 86.9 86.5 86.5 88.9 89.8

BP 91.5 91.5 92.0 92.3 90.9 89.5 88.1 87.9 89.1 91.5

You will need to use two lines and therefore have a key or legend.

(a) Draw a line graph that shows the price changes for each ofthe two companies.

(b) Describe the trends in the prices for the two companies.

5. The graph here showsPerth’s daily solarradiation.

The units of radiation areMj/m2 per day.

(a) What is the lowest level and in what month does it occur?

(b) Describe the trend in the graph.

(c) If levels over 25 Mj/m2 per day are considered unsafe, during what periodis Perth’s radiation unsafe?

(d) The radiation level would be changing daily. What value do you thinkwould be used to represent the levels for a month?



Source: Health Dept of WA

6. This graph shows the percentage of students who consumed alcohol in the lastweek.

(a) Why are there six lines on the graph?

(b) Explain what the vertical axis represents.

(c) In which age groups has the use of alcoholdeclined from 1984 to 1999?

(d) In which survey year do you think the overall usagewas lowest?

(e) What is different about the trends for the period 1996 to 1999?

(f) Describe at least three positive points that the Health Department could findin this data.

(g) Use the graph to estimate the results for each age group from the survey for2002.

(h) Give a possible reason for the low point in the graph in 1993.



1. 2. 3.

4. 5. 6.

7. 8. 9.

Exercise 2: Interpreting Graphical Trends

For each of the sketch graphs shown here explain what the graph is showing in terms ofthe two quantities.



Exercise 3: Scatter Graphs

1. The following data is heights (cm) and weights (kg) of 15 AFL Footballers.

Height 183 197 189 180 192 181 183 186 190 175 184 184 192 179 193

Weight 76 104 82 74 87 79 74 83 95 78 82 80 92 82 98

(a) Draw a scatter graph to represent this data.

(b) Describe the pattern in the scatter graph and any relationship it shows.

(c) What does the scatter graph show in terms of height and weight?

2. The data in this table shows the germination time of seeds (days) at different soiltemperatures (EC).

Temp. 10 12 14 16 15 16 12 11 17 11 12 14 11 13 18 16

Time 8 5 3 3 2 4 4 5 1 6 6 5 7 4 2 2



(c) What does the scatter graph show in terms of soil temperature andgermination time?

3. This table shows games lost and points scored by netball teams in a competition.

Losses 1 2 2 3 4 4 6 7 7 9

Points 16 14 14 12 10 10 6 4 4 0



(c) If two points are awarded for a win why would this relationship benegative?

(d) Why would this relationship be a straight line?



4. The table shows the sugar (g) and Energy (kJ) contained in 100g of eight breakfastcereals.

Sugar 1.8 3.5 2.7 2.9 2.5 3.7 2.8 2.8

Energy 1197 1596 1533 1436 1395 1750 1390 1490



(c) What does the scatter graph show in terms of sugar and energy levels inbreakfast cereals?

(d) Use the scatter graph to estimate the energy levels for breakfast cereals

containing: (i) 2.0g of sugar per 100g (ii) 4.0g of sugar per 100g

5. A basketball fan had a theory that the more fouls you made in a game the morepoints you would score. He backed up his theory by pointing to the positiverelationship between these two quantities. An example of the relationship isshown in this table of players in a game between the Wildcats and the 36'ers.

Fouls 3 1 5 3 3 2 1 0 5 0 5 3 0 1 0 3 2 3 4 0

Points 8 7 10 8 18 14 2 0 14 0 7 15 10 7 0 9 4 26 15 0



This positive relationship implies that when fouls are high so are points scored.

(c) Does this support the fan’s theory?

(d) What other quantity would cause fouls and points scored to be high at thesame time?

6. There is a strong negative relationship between the occurrence of car accidentsand the distance from a person’s home.

(a) What does this mean?

(b) What other quantity could affect this relationship?



Exercise 4: Travel Graphs

The Southorn family and the Power family both head off for a day at the beach atMandurah. The travel graph here shows their two journeys.

1. Which sequence of points shows the journey of the Power family?

2. What time do both families leave from home?

3. Who gets home first?

4. Who stays the longest at the beach?

5. How far is the beach from their homes?

6. When are both families at the beach together?

7. What does a flat (horizontal) section of the graph mean?

8. How long did the Powers stop for on the way home?

For most sections of the journey both families travel at 80km/h.

9. What is the Southorn’s speed from C to D?

10. Which section do the Powers travel at 100km/h?

11. How can you pick this ‘fast’ section from the graph?

12. Which section do the Southorn’s travel at 60km/h?

13. How can you pick this ‘slow’ section from the graph?

14. Name two sections of the graph that are parallel.



Puzzle:

Australian HighwaysBreaking the code in this puzzle will give you the names of sixhighways you can travel around Australia.

In these travel graphs the time is in hours and the distance is in kilometres.

1. Which graph shows a person walking?2. Which graph shows a person travelling by bike?3. Which graph shows a person travelling by car?4. Which graph shows a person travelling by plane?Which section of a graph shows,5. a person returning to arrive home after 3 hours?6. a person starting to return home at the same speed as they were leaving?7. a person stationary for 60 minutes? 8. a person continuing to walk away from home after a break?9. a person 800km from home?10. a person travelling away from home at 20 km/h?11. a person leaving home at 5 km/h?12. a person travelling at a speed of 90 km/h?13. a person travelling at a speed of 60 km/h?14. a person taking a 30 minute break before continuing at the same speed?15. the fastest speed of any of the journeys?

Code Boxes:

14 8 15 14 5 10 4 13 6 14 11 11

12 11 9 12 3 8 2 12 13 10 7 10 13

9 12 15 15 10 14 15 9 15 1 13 14



Application A: Material required: Excel software package

Predicting Water Storage

In this application the object is to graph known data about water storage indams and use this graph to make predictions about future water storage levels. The data is the number of gigalitres stored in Perth dams over three years.

Task 1: Start up Excel. A new spreadsheet should be open to you.

Task 2: For headings type “Perth Dam Storage” into cell A1 and “(Gigalitres)” intocell A2.

Task 3: Enter the data from the table below into the spreadsheet. The years godown the first column from cell A5 to cell A7. The months go across fromcell B4 to cell M4. The data is then filled into the cells from B5 to M6.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1999 216 192 171 156 144 144 150 174 225 255 255 240

2000 219 204 183 171 162 153 198 246 273 303 288 270

2001 246 222 201 180 171 165 159 165 174

Task 4: Now select the data you are going to graph by clicking the left mousebutton while holding the cursor over cell A4, holding the button down, anddragging to cell M7 before releasing the button.

Cell A4 should be white but all others cells should be shaded (selected). Itwill look like this screen shot.



Task 5: We now need to create the graph. To do this click on an icon in thetoolbar that looks like a graph or click on Insert on the menu bar and selectChart . This should open a dialogue box which includes a choice of charts(graphs).

Task 6: Select Line and then click on Finish to have your graph drawnfor you. A line graph will be a good way to follow thetrends in water storage. Once it is drawn you can changethe size of the chart box by clicking on a black square on theframe and dragging it out or in.

Task 7: Click on Chart in the menu bar and select Chart Options. (If Chart is notavailable on the menu bar it is because the chart is not selected. Click onthe chart frame once to select it.) A dialogue box will open that allows youto put in a title. Type in a title from the information and put your initialsafter the title (to identify it if you print). You can also label the axes at thistime. While in this dialogue box you can choose other tabs to further edityour graph. Make any changes here to suit your requirements then click onOK to close the dialogue box.

Task 8: Check what your graph will look like when printedby clicking on File in the menu bar and choosingPrint Preview. To preview just the chart it needs tobe selected. Print out your graph at this point.

Task 9: Comment on the water storage patterns in Perth’s dams for these threeyears. You should discuss the trend for each year as well as comparingthe three years.

Task 10: Your final task for the rainfall data is to predict the storage for October,November and December 2001 under two types of conditions.

First: Assuming Perth gets some late rainfall as in 1999 and 2000draw in the rest of the graph for 2001.

Second: Assuming Perth gets no late rains draw in the rest of the

graph for 2001. (Use a different colour here and add alegend to show these two sets of predictions).



Task 11: Start a new spreadsheet and enter the data in this table:

Exchange Rates for US ($) and Japanese Yen against the Australian dollar.

28-Aug 12-Sep 15-Sep 16-Sep 22-Sep 28-Sep 6-Oct 7-Oct 10-Oct 12-Oct 13-Oct

Japanese (Yen) 64.38 62.41 61.63 62.00 57.56 58.11 60.43 60.90 61.02 60.66 61.06

US ($) 0.53 0.51 0.52 0.52 0.49 0.49 0.50 0.50 0.51 0.50 0.50

Task 12: Select only the dates and Japanese (Yen) data. Use the Chart Wizard toconstruct the line graph for this data only.

Task 13: The dates on the data are not regular. How does Excel deal with this? Why is this correct?

Task 14: Now select all of the data. Complete step 1 of the Chart Wizard byselecting line graph and clicking on Next. Look at the preview in step 2 -what is the problem with showing both exchange rates on the same axes?

Task 15: Click on the Series tab in step 2 and remove the Japanese (Yen) series. Then complete the steps of the Chart Wizard to get a graph showing onlythe US ($) rates.

Task 16: Start another new spreadsheet and enter the data in this table:

Stock Exchange Share Prices

Company Code Fri 5th Oct

Mon8th Oct

Tues9th Oct

Wed10th Oct

Thu11th Oct

Fri 12th Oct

Coles Myer CML 6.87 7.07 7.40 7.38 7.48 7.68

Telstra TLS 5.20 5.11 5.25 5.13 5.12 5.07

BHP Billiton BHP 9.24 8.84 8.95 8.87 9.24 9.56

P & B Ltd PBL 9.17 8.99 8.94 9.00 9.33 9.30

Western Mining WMC 7.90 7.61 7.79 7.64 7.76 8.45

Task 17: Use the Chart Wizard of the Spreadsheet to construct a line graph for thedata.

You can find a link to an Australian Stock Exchange web page that gives recent shareprices and a line graph of share price changes at this page of the OTRNet web site:http://www.otrnet.com.au/IntegratedMathsModules/D01/D01TLR.html



Application B:Material required: Excel software package

Temperature Relationships

The first part of this application looks at the relationship between the maximum andminimum temperatures for cities of the world.

Task 1: Explain what type of relationship you would expect to find betweenmaximum and minimum temperatures.

Task 2: Start up Excel. A new spreadsheet should be open to you.

Task 3: For headings type “World Temperatures” into cell A1 and “(September 28,2001)” into cell A2.

Task 4: Enter the data from the table below into the spreadsheet. Maximum goesin cell A4, minimum in cell A5. The values are entered from cell B4 to cellX5 as in the table:

Max 18 28 19 29 24 17 31 17 17 31 17 32 20 20 9 18 19 23 30 26 14 18 17

Min 13 19 10 24 13 10 27 14 10 27 4 25 12 17 0 14 11 13 25 20 8 10 13

Task 5: Now select the data you are going to graph by clicking the left mousebutton while holding the cursor over cell A4, holding the button down, anddragging to cell X5 before releasing the button. Cell A4 should be whitebut all others cells should be shaded (selected). It will look like this screen shot.

Task 6: We now need to create the scatter graph. To do this click on the icon inthe toolbar that looks like a graph or click on Insert on the menu bar andselect Chart. This should open a dialogue box which includes a choice ofgraphs.



Task 7: Select Scatter and then click on Finish to haveyour graph drawn for you. A scatter graphallows us to look for relationships betweentwo quantities. Once it is drawn you canchange the size of the chart box by clicking ona black square on the frame and dragging itout or in.

Task 8: You will need to put a title on the graph and label the axes. Click on Chartin the menu bar and select Chart Options. (If Chart is not available on themenu bar it is because the chart is not selected. Click on the chart frameonce to select it.) A dialogue box will open that allows you to put in a title. Type in a title from the information and put your initials after the title (toidentify it if you print). You can also label the axes at this time. While inthis dialogue box you can choose other tabs to further edit your graph. Remove the legend as this is not appropriate for a scatter graph. Makeany changes here to suit your requirements then click on OK to close thedialogue box.

Task 9: Check what your graph will look like when printedby clicking on File in the menu bar and choosingPrint Preview. To preview just the chart it needs tobe selected. Print out your graph if required at thispoint.

Task 10: Comment on the relationship that is shown in the scatter graph.

Task 11: Explain what this relationship means in terms of the maximum andminimum temperatures.

In the next series of tasks we are looking to see if there is a relationship between theamount of times a ball number is drawn from barrel A and barrel B of Powerball Lotto.

Task 12: What type of relationship do you predict?



Task 13: Start a new spreadsheet and enter the data in the table here:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Barrel A 24 29 32 29 39 26 34 35 32 28 27 33 34 29 40 33 36 25 37 36 27 35 31 34 36 30 32 30 31 27 24 22 35 26 32 24 34 30 35 30 36 26 30 30 35

Barrel B 6 5 8 9 4 7 7 4 1 8 4 6 4 3 8 5 6 9 8 7 3 3 4 10 3 12 7 6 6 7 8 6 10 8 4 3 5 8 8 5 3 4 6 9 13

(The data can be downloaded from the following web address instead oftyping it in: http://www.otrnet.com.au/IntegratedMathsModules/D01/D01TLR.html )

Task 14: Use the Chart Wizard of the Spreadsheet to

construct a scatter graph for the data.

Task 15: Comment on the relationship that is shown in thescatter graph.

Task 16: Explain what this relationship means in terms ofthe number of times drawn from Barrel A and Barrel B.

In the next series of tasks we are looking to see if there is a relationship between heightand weight of AFL footballers.

Task 17: What type of relationship do you predict?

Task 18: Start another new spreadsheet and enter the data in this table:

Height (cm) 175 182 200 177 190 192 210 172 191 183 191 192 175 182 181 192 190 183

Weight (kg) 79 83 94 71 91 94 102 72 90 79 86 90 78 83 87 87 85 81

Task 19: Use the Chart Wizard of the Spreadsheet to construct a scatter graph forthe data.

Task 20: Comment on the relationship that is shown in the scatter graph.

Task 21: Explain what this relationship means in terms of the height and weight offootballers.

Application C:



Material required: Graphics calculator

Graphics calculators are capable of drawing scatter graphs and at the same time cancalculate summary values like the mean. The statistics calculated also include a valueknown as the correlation coefficient which gives a numerical value for the strength of therelationship between the two quantities.

High Marking

Caroline has a theory about football that tall players take the mostmarks. To test this theory she gets the heights of each Collingwoodplayer in a game from the Football Record and then finds the numberof marks taken in the AFL Statistics in the paper.

Task 1: Enter this bivariate data collected by Caroline into thegraphics calculator.

Height (cm) 182 185 180 175 178 188 181 194 189 180 190 198 185 188 190 183 185 183 192 190 199 193

Marks 10 5 0 6 1 3 4 5 3 1 5 4 6 4 4 1 4 1 2 0 1 0

Here is how the data looks on one typeof calculator:

Task 2: Ensure your calculator reads this as bivariate data (2 variable).

Task 3: Setup the scales on the axes for your calculator. Todo this you need to consider the smallest andlargest values for X - the height and Y - the marks.

Task 4: Get the calculator to draw the scatter graph.

Task 5: Comment on any relationship you can see from your scatter graph.



Task 6: Get the calculator to show the summary statistics.

Task 7: What is the mean height of the players?

Task 8: What is the mean number of marks taken?

Task 9: What is the correlation coefficient?

Task 10: Discuss the correlation coefficient and what it means with your teacher.

Task 11: Comment on how this value matches what you wrote in task 5.

Task 12: Comment on Caroline’s theory given this result.

Task 13: Caroline still believes her theory might be correct but decides that the datashe collected was not good enough.

Write down how Caroline might change her data collection to better testher theory.

Task 14: Laurence comes up with a theory that it might be that marks taken arerelated to a players weight rather than height.

Explain the steps you could follow to test this theory.

Explain what sort of results would support Laurence’s theory.



Application D: Materials required: Data from Activity B.

Temperature prediction

Task 1: Using the data collected in Activity B find the following summary values:

Highest maximum temperature:

Lowest minimum temperature:

Greatest daily range in temperatures:

Mean maximum temperature:

Mean minimum temperature:

Median maximum temperature:

Median minimum temperature:

Task 2: Set up a line graph showing the maximum andminimum temperatures for the 14 days. Leaveroom on your graph to add 7 more days.

Task 3: Describe the variation in maximum temperatures over the 14 days.

Task 4: Describe the variation in minimum temperatures over the 14 days.

Task 5: By following the trends for the 14 days you have recorded, predict themaximum and minimum temperatures for the following 7 days and showthese predictions by extending your graphs for 7 more days.



Application E: Material Required: A4 paper and graph paper (including cm2).

Misleading Line Graphs

Task 1: The two line graphs shown above represent the same data. What hasbeen done in the second graph to make it look like sales are increasingrapidly?

Task 2: The shire uses the first graph above to show that the number of netballplayers is falling rapidly. The netball association says this is wrong, andshows the second graph. Explain how the shire made the correct valuesshow a different picture from the real situation.



Task 3: Draw up two grids on cm2 paper as shown in the diagrams here.

Task 4: Represent the temperature data in this table on both grids.

Time (a.m.) 6 7 8 9 10

Temperature (EC) 9 12 18 25 28

Task 5: Comment on the different picture presented by the data in the two graphs. Explain what causes this difference.

Task 6: You are trying to get people to invest in yoursoftware business “Insane Games” by makingyour profits look like they are increasing rapidly.

Make an A4 size advertisement to promote yourbusiness using a line graph to positivelypresent the data.

The data you have is given in this table:

Year 1994 1995 1996 1997 1998 1999 2000 2001

Profits ($ thousands)

60 66 68 75 81 82 83 95



Application F: Materials required: Newspapers, scissors, glue.

Newspaper Search: Bivariate Data

Task 1: What type of relationship do you think would existbetween the price of used cars and their age?

Task 2: Find an advertisement for used cars in a newspaper.

Task 3: For twenty of these cars record the advertised price and the age of the carin years (be careful - this is how many years since it was made, not the yearit was made).

Task 4: Draw a scatter graph for this data.

Task 5: Comment on the relationship between price and age that your scattergraph shows.

Task 6: Write down one way of improving the datacollection for this activity if you were trying to showthat a cars price was related to its age.

Task 7: Find and display two examples of line graphs from newspapers.

Task 8: Alongside each graph explain what the graph is showing and describe anytrends shown in the graphs.



Application G:

Project: Finding relationships

For this project you are going to write a report on the relationship between twoquantities.

Task 1: Look back over Activity E to get an understanding of what this projectinvolves. What you are going to do will be similar to that activity.

Task 2: Select the two quantities that you are going to look for a relationshipbetween. Some examples are given here or you can make up your own.C Predicted temperature v actual temperature C CPU size v Price on computersC Results in maths v results in scienceC Test results v heightC Age v weightC Or choose two quantities you would be interested in looking at

Task 3: Think through and plan how you would cover these points for your choice. C What data needs to be collected?

C How can you collect the data?C How are you going to record and organise the data?

If you can’t work out how to cover any of these points you may need to goback to task 2 and choose a new pair of quantities.

Task 4: Review your progress with your teacher.

Task 5: Commence your report by explaining what relationship you areresearching and what you expect to find.

Task 6: Collect the data necessary for your research.

Task 7: Organise and display the data you have collected.

Task 8: Complete your report by writing about the relationship you foundbetween the two quantities. Try to explain why (or why not) a relationshipexists.

Comment on these points if you can:C What data might have been better to collect?C What other factors affect the relationship between the quantities?C Did your results match your predictions?



Student Reflection

What have I learned in this module?

What new words did I learn during this module?

Look at the outcomes at the start of the module (page 3). Have I progressed on each ofthese outcomes?

What do I need to improve on?

Write about one thing in this module I found interesting.

What do I think was the most important concept in this module?

Where could the maths in this module be used in our society?

One area I would like to look more at is:

Write something about how the bits in this module connect to each other.

Write something about how the bits in this module connect to other modules.



ANSWERS TO EXERCISES:Any graphs should be checked and discussed with another student or your teacher.

Exercise 1:2. (b) The attendance rate fall to a low at August and then increases again. (c) -92%3. (b) Reverse the direction. (c) There is a steady rise to a peak then a rapid drop off.4. (b) Both companies prices show a rise until day 4 then a rapid fall to day 8 after which they begin to rise

again. Gull’s prices are lower on most days.5. (a) 13.0 in June

(b) A smooth decrease to a low in June followed by a smooth rise to a high in December. (c) The period October to March would have unsafe radiation levels.(d) The value could be the mean (or median).

6. (a) One for each age group.(b) This is the percentage of the age group that consumed alcohol in the last week.(c) 12 and 13 year olds.(d) 1993(e) 16 and 17 year olds are opposite the trend for other age groups.(f) The drop off for 12 and 13 year olds, the decreases from 1987 to 1993, etc(g) Estimates only: 12 = 16%, 13 = 30%, 14 = 38%, 15 = 46%, 16 = 50%, 17 = 60%(h) Possible reasons: an advertising campaign, an education campaign etc

Exercise 2:1. Height increases with age at first but then levels off at a fixed height.2. Running speed increases with age to a maximum and then drops off steadily to old age.3. As the price increases sales decrease.4. As sales increase profit increases, slowly at first but then more rapidly.5. As price increases profit increases to a maximum point and then decreases.6. As time goes by the crowd increases steadily before levelling off then decreasing rapidly.7. During the year the average temperature fall smoothly to a low point then rises smoothly.8. The temperature starts the day negative but then rises steadily to a high before falling back.9. As weight increases price is constant for a while then jumps to new (higher) levels.

Exercise 3:1. (b) The points are clustered around a line showing a strong positive relationship.

(c) The trend is for taller players to weigh more.2. (b) The points are clustered around a line showing a strong negative relationship.

(c) The higher the soil temperature the lower the germination time.3. (b) The points are on a line showing a perfect negative relationship.

(c) Because it is between losses and points - higher losses leads to lower points.(d) There is a fixed 2 points per win.

4. (b) The graph shows a strong positive relationship.(c) The higher the levels of sugar the higher the levels of energy present.(d) (i) 1255 (ii) 1776

5. (b) The graph shows a medium strength positive relationship.(c) Both values are high together but this is because of other factors.(d) Time on court, level of involvement in play.

6. (a) The closer you are to home the higher the chance of a car accident.(b) The amount of time spent driving near your home.

Exercise 4:1. APQRST 2. 8am 3. Powers 4. Southorns 5. 120km6. 10am to noon 7. Not moving 8. 45min 9. 80km/h 10. Q to R11. Steepest section 12. A to B 13. Has least slope 14. CD to EF or to ST


Students’ Integrated Maths Module for Bivariate Data 1 · [SIMM] Bivariate Data 1 3 Introduction...

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Transcript of Students’ Integrated Maths Module for Bivariate Data 1 · [SIMM] Bivariate Data 1 3 Introduction...