ata management - correspondence studiescsp.ednet.ns.ca/documents/sample_lessons/grade_10/... ·...

UNIT 1

DATA MANAGEMENT

LEARNING OUTCOMES:

Upon completion of this unit, you are expected to be able to:

gather data, plot data using appropriate scales, and demonstrate an understanding ofindependent and dependent variables and domain and range

design and conduct experiments using statistical methods and scientific inquiry

demonstrate an understanding of concerns and issues that pertain to the collection of data

describe real-world relationships depicted by graphs, tables of values, and writtendescriptions

solve problems by modeling real-world phenomena

determine the accuracy and precision of a measurement

determine and apply formulas for perimeter, area, surface area, and volume

calculate various statistics using appropriate technology, analyze and interpret displays, anddescribe relationships

analyze statistical summaries, draw conclusions, and communicate results about distributionof data

determine whether differences in repeated measurements are significant or accidental

explore measurement issues using the normal curve

calculate and apply mean and standard deviation, using technology to determine if variationmakes a difference

create and analyze scatter plots using appropriate technology

determine and apply the line of best fit using linear regression with technology

construct and analyze graphs relating two variables

use interpolation and extrapolation and equations to predict and solve problems

MATHEMATICS 10

PAGE 16 CORRESPONDENCE STUDY PROGRAM

DATA MANAGEMENT

UNIT 1 INTRODUCTION:In today's society we are often over-burdened with an abundance ofinformation and numbers concerning various topics which may or may notbe relevant to one's everyday life. This information is often used to makedecisions. There is a need to manage information overload in an efficientmanner to aid in the decision making process and ensure that informationoverload does not occur. This gives rise to one of the newest branches ofmathematics known as data management or statistics. Studying datamanagement provides us with the necessary knowledge, skills and attitudeto collect, organize, represent, display, and analyze data in both an efficientand effective manner. Overall, you will learn when a data set has a pattern,it can be modeled and verified using mathematical representation such asstatistical measure, a graph, or a function. In addition, you will explore yourlevel of confidence in this representation and any predictions or conclusionsyou draw about the data.

UNIT 1

CORRESPONDENCE STUDY PROGRAM PAGE 17

SECTION 1: VARIABLES AND

RELATIONSHIPS

In this lesson you will look at the concept of a

variable and relationships between variables in

more detail. In any relationship, factors that

change are called variables. When a change to one

variable causes a change in another variable, a

cause-and-effect relationship exists between the

variables. The independent variable is a factor that

affects another factor in an experiment or

relationship. The dependent variable is the factor

that is affected by other factors in an experiment

or relationship.

Scientists carefully design experiments to

study which factor has the greatest effect on a

particular situation. An independent variable

is selected to study and an experiment is

designed to change only that variable. All

other variables are held constant. A

controlled variable is any independent variable

whose value is held constant during

an experiment. A controlled experiment is

any experiment in which all but one

independent variable is controlled.

The example problem and solution can be used

as a guide when answering questions involving

relationships.

EXAMPLE PROBLEM

Curling recently became a Winter Olympics

event. The team with the closest rocks to the

center scores in each end of play.

1. The distance the rock moves down the ice

is the dependent variable. It depends on

other factors.

2. Many factors might affect the distance the

rock moves down the ice. Three factors

include:

a) the ice maker's decisions

b) the curler's decisions

c) chance, events outside anyone's control

The dependent variable is affected by the speed

the curler throws the rock, while, the independent

variables are factors which are not affected by the

speed of the rock.

MATHEMATICS 10


The factors a), b), and c) are independent of the

distance the curling rock attains. The table below

displays independent factors not affected by the

distance the curler throws the rock.

decneulfnisrotcaFrekameciehtyb

decneulfnisrotcaFrelrucehtyb

,srotcafecnahCedistuostneve

lortnocsenoyna

ecifossenilnaelc moorbfongiseddetceles

nospilsrelrucaecieht

"gnilbbep"eci rofdetcelesseohsgnidils

esionnaf

ecifoerutarepmet desueuqinhcetkcah-eht-fo-tuo

ecifossenilnaelcstratsyalpretfa

ytidimuh ehtmfroedilgehtkcah

ehtmorftaehnisnafforebmun

knireht

Mind Map: There are more factors you may

included in the curling example. The diagram

below requires you to develop three additional

independent variables as factors which are not

affected by the distance the curler’s rock is thrown.

See “Focus A, Cause and Effect Relationships” on

page 2 of the text. Complete the following

mind map.

READ AND DO 1

In Mathematical Modeling, Book 1, read

pages 2 to 6. Complete Check Your

Understanding problem 5, page 5 and problem

7, page 6 in the text.

PRACTICE PROBLEM:

Do the following problem for practice and check

your answers in the Solutions Appendix at the

back of this manual.

1. a) List some factors that may affect the speed

at which a parachuter falls to the ground.

b) Identify the factors in which the

parachuter has control over from part a).

Mind Map of Factors that Affect the Curler's Shot Distance

Curler's Shot Distance

DO AND SEND

UNIT 1


SECTION 2: MEASURING

Students are required to collect data in many

situations. The information is analysed,

interpreted and used to calculate additional

information. Two important considerations

student must be mindful of when taking

measurements are accuracy and precision.

Students may generate significant digits using

measurement tools with finer scales. The finer the

scale used to measure, the greater number of digits

a student may record. “Focus C: Accuracy and

Precision”, page 8 permits you to distinguish

between accuracy and precision. Read page 9

under “Counting Significant Digits” and the right

hand column information to learn more about

significant digits. Significant digits will be used in

senior high school science courses.

EXAMPLE PROBLEM

A rectangle, 2.13 by 6.49 is provided with the

dimensions labelled. You are to find the perimeter

and area of the rectangle. The answer is to be

expressed with the appropriate level of precision.

The rules of significant digits are provided with

the examples given:

2.13 cm

6.49 cm

6.49 cm

2.13 cm

Perimeter = 6.49 + 6.49 + 2.13 + 2.13 = 17.24

The answer should be expressed as 17.24 cm. The

least precise value in the problem is the

hundredth’s position.

Area = (6.49)(2.13) = 13.8237

Using the rule for multiplication, you express the

answer as 13.8 cm2. The least number of

significant digits in the factors is three.

RULES OF SIGNIFICANT DIGITS

1. all non-zero digits are considered significant2. any zero located between two significant

digits is considered significant

NOTE:

Leading zeros are not counted when countingsignificant digits and trailing zeros are usuallycounted when they occur after the decimalpoint. Trailing zeros may or may not becounted.

EXAMPLES:

21.7 there are 3 significant digits0.0037 (leading zeros) 2 significant digits1078 there are 4 significant digits350 2 significant digits350.0 (trailing zero after decimal)

4 significant digits10.0034 6 significant digits

ADDITION AND SUBTRACTION

In addition or subtraction you add or subtractthen round the product to the least precisedecimal place or place value.

EXAMPLES:

9.63 + 5.278 + 8.52 = 23.428 = 23.4314.52 - 4.06 = 10.46124.24 + 2.25 = 126.4912.0 + 7.59 = 19.59 = 19.6

MATHEMATICS 10


PRACTICE PROBLEM:




1. Give the answer to each of the following in the

appropriate level of precision (i e. significant

digits)

a) 19.02 + 3.015 + 0.0020

b) 3.0 × 12.6

c) 102 - 2.65

d)

e) 300 + 106

f ) 0.2 × 105

0.00305

0.00021

MULTIPLICATION AND DIVISION

In multiplication and division you multiply or

divide then round the product to the least

number of significant numbers.

EXAMPLES:16.4 × 4.4 = 72.16 = 72

16.3 × 2.19 = 35.697 = 35.7

16.3 × 0.18 = 2.934 = 2.9

16.3 × 5.34241 = 87.081283 = 87.1

READ AND DO 2

In Mathematical Modeling, Book 1, readpages 8 to 11. Complete Check YourUnderstanding problems 13, 14, 16 and 18 onpages 11 to 13 in the text.

You should read the Review of key chapterterms and concepts on pages 47 - 51.

UNIT 1


SECTION 3: DESCRIBING DATA

To make decisions, students need ways to describe

a large set of data. On page 14, read section 1. 3“Describing Data”. A large set of data may be

described using an average. You recall an average is

a single value, calculated from all values in a set,

and used to represent the general significance of a

set of values. In the left column of the text, page

14, the term average is explained. You should

become familiar with the terms mean, median,

and mode. Read “Focus E, Average - A Single

Number Used to Describe or Represent a Set of

Data”, page 15.

The following examples demonstrate mean,

median and mode. These are measures of average.

They are called measures of central tendency. Not

all sets provide useful measures of central

tendency.

MEAN EXAMPLE

The set of numbers include:

8 + 7 + 12 + 4 + 6 + 5 = 42

Adding the set numbers provides a totalof 42.

Dividing the total of all set numbers by 6,(there are six numbers in this set) equals42 ÷ 6 = 7. The number 7 is the singlevalue, calculated by dividing. It representsthe general significance of the set ofnumerical values. The mean number is 7.

MEDIAN EXAMPLE


1, 2, 4, 6, 8, 10, 12

The median is 6. It is the middle number.If there are an even set of numbers themedian is the mean (average) of the two"middle" numbers.

MODE EXAMPLE


1, 2, 4, 6, 8, 8, 8, 8 10, 12

The mode is 8. It is the most frequentlyoccurring number in the set.

EXAMPLE PROBLEM

This set demonstrates how a mean measure of

average can provide an inaccurate measure of

central tendency.

Bart, Bill, Bob, Betty and Barry work for Star

Central. Bart is an accounts payable clerk. He

earns $25 000 annually. Bill is a technician. He

earns $30 000 annually. Bob, in design, earns

$35 000 annually. Betty is the plant manager

earning $45 000 yearly and Barry is the company

president earning $400 000 annually. The mean

salary is $107 000. The company president's

salary skews the result. Barry's salary is an example

of an outlier.

MATHEMATICS 10


Outliers do not provide an opportunity to calculatean accurate measure of central tendency.

In “Focus F, Data Distribution - Stem-and-LeafPlots”, on page 17, you learn why data is presentedin this format and how a stem-and-leaf-plot isarranged.

Arrange the data in the table below in a stem-and-leaf plot. Place your results in the following stem-and-leaf plot.

3.11 6.21 9.31 2.41 7.51 8.61

4.91 5.61 7.11 3.91 8.91 9.11

4.21 7.41 0.21 1.11 2.31 2.61

7.31 1.61 5.11 1.41 8.91 6.11

2.21 1.31 5.41 3.81 9.61 8.81

Turn to page 18 in Mathematical Modeling andread “Focus G - Box and Whisker Plots”.

Box-and-whisker plots show the distribution andrange of data around a median. Explicit articles are

not shown in the data. The data does show lower

and upper data values and permits the

development of a median in the lower and upper

quartile.

The term outlier was examined in the opposite

column. Outliers may influence results when

confirming the median in a box-and-whisker plot.

Examine the box-and-whisker plots a) and b)

below.

Read “Investigation 2, Reaction Time” on page 14.

The data below was generated following the

procedure in Investigation 2. What is the typical

reaction time in box-and-whisker plot a)? In b)?

210 24

4214

39

2719

a)

b)

16

In a), the typical reaction time is 14. In b), the

typical reaction time is 16. The outliers in box-

and-whisker plot a) are 2 and 42. Are there

outliers in box-and-whisker plot b)? The answer is

yes; the numbers 3 and 27 are outliers in b).

What are the range of values where the middle

50 per cent of the data is distributed? In a), the

range of values where the middle 50 per cent of

the data is distributed is 10 and 24. In b), the

range of values where the middle 50 per cent of

the data is distributed is 9 and 19.

DO AND SEND

metS faeL tnuoC

11 976531 6

21

31

41

51

61

71

81

91

UNIT 1


READ AND DO 3


pages 14 to 23. Complete Focus Questions 3, 9,

10, and 11 on pages 16-20 and Check YourUnderstanding problem 14 on page 21 in

the text.

Complete the following problem. Jamison

surveyed his classmates to find the number of

kilometres each person lives from the school.

Jamison learned his twelve classmates live the

following distances from the school.

You are to complete a box-and-whisker plot below.

Use the data given above. Indicate whether there

are outliers in the data and the range of kilometres

most students live from the school.

8 21 1 3 7 5 0 62 4 2 6 41

To complete the problem above, first calculate the

median, the lower quartile and the upper quartile.

Place each of these numbers and outliers in the

box-and-whisker plot above. Complete a sentence

stating your findings.

SOCCER DISTANCE PROJECT

This project is modeled on the procedure in

Investigation 2 - Reaction Time page 14 of the text.

You organized 40 students to kick a soccer ball.

Each student kicked the soccer ball once. The data

is recorded in table below. The distance measured

is in meters.

kciK#

tnedutSecnatsiD

kciK#

tnedutSecnatsiD

kciK#

tnedutSecnatsiD

kciK#

tnedutSecnatsiD

1 2.41 11 2.5 12 2.81 13 2.51

2 3.21 21 3.81 22 7.91 23 3.71

3 1.51 31 7.51 32 1.71 33 1.61

4 7.81 41 0.31 42 4.11 43 4.71

5 5.41 51 3.91 52 3.91 53 3.61

6 1.31 61 8.71 62 6.31 63 8.61

7 9.61 71 4.41 72 2.02 73 9.51

8 8.21 81 8.61 82 0.42 83 5.02

9 6.51 91 6.61 92 1.41 93 6.81

01 3.61 02 3.91 03 8.31 04 9.71

1. Determine one value that you believe best

determines the distance you will probably

kick the soccer ball. The number you

determine describes your average performance.

This is the distance that you typically kick the

soccer ball.

2. Use the first twenty kicks as the distance you

kicked the soccer ball twenty times. Calculate

the average distance you kicked the soccer ball

with the average distance your forty classmates

kicked the soccer ball. Reflect on the various

ways you used to calculate the average

distance. Write a paragraph to explain the

different methods used to calculate the

average distance.

The data set, given above, is not organized. When

each student kicked the soccer ball the distance

was recorded. When the data is organized you may

begin to see a pattern in the data. You may begin

SOCCER TABLE

DO AND SEND

MATHEMATICS 10


to see how the values are spread or distributed. Use

the stem-and-leaf plot below to organize the data.

This will make it easier to look for patterns and to

analyze the data. The data is ordered from the least

distance the soccer ball travelled to the greatest

distance. The range of the data is found by

calculating the difference between the least and

greatest distance the soccer ball travelled. You may

begin to see how the values are spread or

distributed by the "shape" of the plot.

metS faeL tnuoC

5

11

21

31

41

51

61

71

81

91

02

42

3. The data in the stem-and-leaf plot you created

is clustered. Examine the data and indicate

where the data is clustered.

a) List the two kicks representing the least

distance the soccer ball travelled?

b) State the two kicks indicative of the

greatest distance the ball travelled.

CREATING A BOX-AND-WHISKER PLOT

4. In the diagram below, there are five number

lines. Use the data from the Soccer Table and

follow steps a) through e) to complete the

number lines with the required information.

Upperextreme

5 10 15 20 25

5 10 15 20 25

5 10 15 20 25

5 10 15 20 25

5 10 15 20 25

1.

2.

3.

4.

5.

Lowerextreme

a) On number line 1, draw an arrow fromthe box marked “Lower extreme” to thepoint on the number line representing thelower extreme and draw an arrow from thebox marked “Upper extreme” to the pointon number line 1 representing the upperextreme.

b) Calculate the median of the data in theSoccer Table. Mark the median on numberline 2.

c) On number line 3, find and mark thelower quartile.

DO AND SEND

DO AND SEND

UNIT 1


d) On number line 4, find and mark the

upper quartile.

e) On number line 5, show where the middle

50 per cent of the data is located.

Construct a box similar to the one below.

Use that box to illustrate where the middle

50 per cent of the data is located.

f ) Now, complete the box-and-whisker plot

below using the Soccer Table data. Your

response should look similar to illustration

13.a) on page 20 of MathematicalModeling, Book 1.

Read Focus H, Data Distribution– Histograms,page 22. The frequency table below illustrates a

bin size of 6 (7 - 1) and the frequency of

distribution of data values within each bin. In the

bin shown, there are 7 data values in the group of

data values.

whisker plot. These plots show how the SoccerTable data is distributed or spread.

The Soccer Table has many pieces ofcontinuous data. A histogram, shown below,has values grouped in bins on the horizontalaxis. The frequency of the data within each binis shown on the vertical axis. This permits youto display the data in graph form.

niB ycneuqerF

7-1 7

21

7

41

7 - 13

13 - 19

19 - 25

Freq

uenc

y

Distance (km)

0 7 13 19 25

7

14

In the frequency table below, the bin size is 5.You are to label the graph with the bin size andfrequency and plot the following histogramusing the Soccer Table data.

0

Freq

uenc

y

Distance (m)

5. You manipulated the data in the Soccer Table

to create a stem-and-leaf plot and a box-and-

DO AND SEND

DO AND SEND

niB ycneuqerF

5-0

01-5

51-01

02-51

52-02

MATHEMATICS 10


6. Now you will begin to describe the data in the

Soccer Table to compare the distances the

soccer ball was kicked. To describe the data,

calculate the mean and median and use a red

pen to mark each on the histogram you

completed in question 5. Describe the

placement of the values? Are they close, far

apart, identical?

Another way to comment on the distribution

of the set of data is to develop a scale. The

scale is used to rate how the set of values is

distributed. Use the following 0 to 10 scale to

rate how the set of soccer distance kicks is

distributed.

SCALE

0 - no distribution of values

3 - the distribution of values is closely

clustered

5 - spread out to some extent but still

appearing clustered

7 - spread evenly across the range with

outliers

10 - spread with little evidence of clustering.

7. Compare the stem-and-leaf plot and the box-

and-whisker plot you created using data in the

Soccer Table.

READ AND DO 4


pages 24 to 26. Complete Check YourUnderstanding problems 22, 23 and 28, on

pages 24 and 26 in the text.

PRACTICE PROBLEM:




1. The mass, in kilograms, of suitcases at the

airport are given in the following table.

51 1 02 7 51 8 3 02

8 61 3 4 31 71 02 9

6 61 22 21 6 91 7 9

01 51 9 81 91 51 41 51

2 82 01 71 7 01 8 8

a) Find the mean, median, and mode for

this data.

b) Create a frequency table for this data

starting at zero and using a bin size of 5.

c) Construct a histogram for the above data

using the frequency table created in part b).

UNIT 1


SECTION 4: DATA SPREAD

DEFINED

Read 1.4 Defining Data Spread, pages 27 to 32, in

your Mathematical Modeling text book. Turn to

page 50 and read the example for 1.4 Defining

Data Spread.

Read Focus I, Standard Deviation: A Measure of

Variation for an introduction to the concepts of

dispersion and standard deviation. See the right

column on page 27 in the textbook to review the

definitions of both terms.

An average provides an introduction to a data set

as an initial step to interpret the data. The

distribution or spread of data provides information

on clusters and outliers and permits an analysis of

patterns in data.

Distribution includes the range and variation of

data. When defining data spread you will see

variation in a data set to permit you to write a

description and definition of the variation. In the

Lobster Catch problem below you will apply these

concepts.

LOBSTER CATCH PROBLEM

The captain of a lobster boat conducted a study

over a four week period. The study was to

determine the best two weeks of the month to

catch lobsters. The data collected is displayed in

LOBSTER CATCH

the table above, right.

1. Does the captain catch more lobster in one

two-week period than the other?

Fill in the blanks in the following sentences.

The mean catch for the first two-week period

is _______ .

The mean catch for the second two-week

period is ________.

2. Is the range of catch during the first two-week

period greater than the second two-week

period?

The first two-week period has a range of

catch of __________.

The second two-week period has a range

of catch of __________.

3. Is there more variation in the first two-week

owttsriFkeew

)gk(doirep

owtdnoceSkeew

)gk(doirep

noM euT deW uhT irF taS

6.52 4.91 3.41 4.11 4.31 3.9

3.42 1.81 1.41 7.81 9.51 3.7

7.71 9.61 1.01 8.9 2.11 7.6

7.61 1.41 7.11 9.8 9.21 8.5

MATHEMATICS 10


period to catch lobsters than the second two-

week period?

eulaVataD morfnoitaiveDnaemeht

)eulavatad-naem(

derauqSnoitaiveD

6.52 65.01-=6.52-40.51 5.111

4.91 63.4-=4.91-40.51 0.91

3.41 47.0=3.41-40.51 55.0

4.11 56.3=4.11-40.51 2.31

4.31 46.1=4.31-40.51 96.2

3.9 47.5=3.9-40.51 9.23

3.42 62.9-=3.42-40.51 57.58

1.81 60.3-=1.81-40.51 63.9

1.41 49.0=1.41-40.51 88.0

7.81 66.3-=7.81-40.51 4.31

9.51 68.0-=9.51-40.51 47.0

3.7 47.7=3.7-40.51 9.95

The table below shows the manual calculation

of the standard deviation. The mean is 15.04.

The deviation from the mean is calculated. The

deviation is the distance each data value is from

the mean.

The mean of the squared deviations is 29.2. The

square root of the mean of the squareddeviations is 5.4.

This suggests that selecting any piece of data

randomly from the first two week lobster catch

is on average, 5.4 kg away from the mean

catch. You may use the TI - 82 or 83 to

calculate standard deviation.

Read question 3 on pages 28 and 29 in your

Mathematical Modeling textbook.

4. Complete the table below by calculating the

deviation from the mean and the mean of the


)eulavatad-naem(

derauqSnoitaiveD

6.52 65.01-=6.52-40.51 5.111

mean deviation fromthe mean


)eulavatad-naem(

derauqSnoitaiveD

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

11.875 -

DO AND SEND

UNIT 1


squared deviation. Use the Lobster Catch data

from the second two-week period.

0 6

12

18 24 30

2468

10

12

The best two weeks of the month to catch lobsters

Freq

uenc

y

Catch

0 6

12

18 24 30

2468

10

12

The best two weeks of the month to catch lobsters

Freq

uenc

y

Catch

a) Graph the first two weeks lobster catch

data in the histogram below.

b) The second two weeks lobster catch data is

to be graphed in the histogram below.

5. Show your calculation of the square root of the

mean of the squares for the second two weeks

lobster catch data below.

Standard Deviation = = _________.

6. Compare the variation in the two sets of

data using standard deviation. Which two

week period had a greater variation?

Explain why.

DO AND SEND 1TOTAL POINTS: 35

UNIT 1 ASSIGNMENT 1Do the following questions and send them to

your marker. The point value for each is at the

end of the question.

In your Mathematical Modeling textbook, do

the following questions, pages 4 - 25.

1. page 4, question 4 5 points






7. page 25, question 26.a), b) and c). 8 points

In c), you can omit the part where it instructs

you to draw vertical lines for the mean and

median. For your histogram start with zero and

use a bin size of 10.

MATHEMATICS 10


SECTION 5: LARGE

DISTRIBUTIONS AND THE

NORMAL CURVE

Turn to 1.5 Large Distributions and the NormalCurve on page 33 of the text. Read pages 33 to 39and page 51 to become familiar the mathematicalterms random and frequency polygon.

You may be familiar with the term "the bellcurve". The normal distribution curve is called abell curve. The curve takes it name from the shapeof the curve once data is plotted. As the size ofparticular data sets increase, the graphed data takeson a bell shape.

Companies that conduct public opinion pollingrely on the use of a large sample of data to makereasonably accurate statements about apopulation's views on a particular subject. These

POLLING BIAS

A famous situation where bias entered a pollingsample occurred in the 1948 presidentialelection in the United States. The pollstersfound, from their large sample, that candidateDewey was predicted to defeat candidateTruman by 13 per cent. Truman won theelection by 5 per cent.

Pollster predictions are founded on themathematical understanding that large samplespermit a generalization to be drawn from thesample and applied to the electorate.

Comparing the Shape of Different-Sized Sets of Data.

1. Use the diagram below to create a histogram

0150 170 180 190

2

4

6

8

10

160

Freq

uenc

y

Height (cm)

140 200

Height measurements (cm)Grade 10 girls

0150 170 180 190

5

10

15

20

25

160

Freq

uenc

y

Height (cm)

140 200

Height measurements (cm)Grade 10 girls

30

3. Use a red pen to create a frequency polygon for

the histograms in questions 1 and 2.

4. The mean in Set 1 data is __________.

The median in Set 1 data is _________.

The modes in Set 1 data are ________.

The mean in Set 2 data is __________.

The median in Set 2 data is _________.

The modes in Set 2 data are _________.polls use random sampling to avoid bias.Read pages 33 and 34, Investigation 4,

from Set 1 in Procedure A.

2. Use the diagram below to create a histogram

from Set 2 in Procedure B.

DO AND SEND

DO AND SEND

UNIT 1


5. Write a response to Investigation Questions 1.a)

and b) on page 34.

Read Focus J, The Effect of Sample Size on the Shapeof a Frequency Polygon, on page 34.

In Focus J, you learn that as the sample size

increases (the data values in the set increase) the

histogram, when graphed, will result in a

frequency polygon that is more curved around the

middle of the graph.

See the two example histograms below for an

example of the frequency polygon curve with the

size of a data set. As the bin size decreases, a

frequency polygon will draw more closely to a curve.

The bin size decreases from 6 in the top histogram

to 3 in the bottom histogram.

0 6 18 24 30

2

468

12

Freq

uenc

y

Distribution

These two example histograms show that as the sample size increases the frequency polygon becomes more curved around the middle of the graph

0

5

10152025

Freq

uenc

y

30

3 6 9 12 15 18 21 24 27 30

Distribution

READ AND DO 5


pages 27 to 32. Complete Check YourUnderstanding problems 4, 6 and 8, on pages

30 and 31 in the text.

Read Focus K, Normal Distribution on page 36 tolearn more about the normal curve and propertiesof normal distribution.

1. Do Focus Question 5 and Check YourUnderstanding question 9 on page 37.

2. Complete Check Your Understanding questions10, 12 and 14, on pages 38 and 39.

3. Complete the following five normaldistribution True and False questions.

a) For a normal distribution the mean andmode are the same value. The median isnot the same as the mode but is the sameas the mean.

b) The majority of the data set is clusteredaround the mean.

c) The graph of the data is symmetrical onlywhen the bin size is less than 5.

d) Suppose 420 students enter an paperairplane tossing contest to hit a wall 20 maway. The mean was 15 m and the resultswere normally distributed. The standarddeviation was 2.5 m. The range of flightdistance for 68 per cent of the students istypically 13.5 to 18 m.

MATHEMATICS 10


e) In a normal distribution outliers fall

outside of 2 standard deviations of

the mean.

PRACTICE PROBLEMS:Do the following problems for practice and check



1. A hospital determines that the average stay in

the hospital for pneumonia cases is 7 d with a

standard deviation of 2 d. Assuming a normal

distribution.

a) What percent of the cases stay in between

3 d and 7 d?

b) What percent of the pneumonia cases stay

in longer than 9 d?

2. The Long Life Light Company advertises that

it’s light bulbs have a mean life of 900 h with a

standard deviation of 50 h. Assuming a

normal distribution:

a) What percent of the bulbs will last

between 900 h and 1000 h?

b) What percent of the bulbs will last longer

than 1000 h?

c) If a business purchases 3000 bulbs, how

many can be expected to last less than

850 h?

UNIT 1


SECTION 6: USING DATA

TO PREDICT

Turn to 1.6 Using Data to Predict and read pages

40 to 44. Return to Focus L, Scatter Plots and Linesof Best Fit on page 40 to become familiar the

mathematical terms scatter plot, line of best fit,interpolate and extrapolate. You are now

investigating a relationship between data

representing two variables. You will also be

expected to make predictions about the

relationship between the data values. An

understanding of this information will support

you as you approach the study of functions.

MALE HEIGHT AND AGE

190

170

150

130

110

90

70

50

06 12 18 24 30

Hei

ght

Age

egA )mc(thgieHnaeM

3 55

6 87

9 601

21 811

51 751

81 771

12 381

42 881

72 091

Create a scatter plot of male mean height at each age

Draw a line of best fit

3. Complete Check your Understanding questions

3, 4, 5, 7, 8 and 9 on pages 42, 43 and 44.

4. Complete parts a, b, c, d and e of Putting ItTogether Case Study 1, page 45 regarding

health issues for teenagers.

1. In the Male Age and Height diagram, next

column, the scatter plot of male height and

age is provided. You are to create a line of best

fit to show the relationship between male age

and male height at each age. What is the cause

and effect relationship between male age and

male height? Is it reasonable to extend the

line? Explain. Refer to pages 40 and 41 in the

text before completing your response.

2. Read Investigation 5, Predicting Writing Speedpages 41 and 42 of the text. Complete

Procedure A, B, C, D, E, F, G, and H using the

diagram on the next page.

READ AND DO 5

Complete the following four questions.

MATHEMATICS 10


15

13

11

9

7

5

3

1

03 5 7 9 11

Num

ber

of w

ords

wri

tten

Number of letters in word

Create a scatter plot of of the mean number of words written and the number of letters in a word.

Draw a line of best fit

drownisretteL fo#naeMnettirwsdrow

3

5

7

9

11

PRACTICE PROBLEM 2




1. The following chart shows the final marks in

Math and Physics for 13 students.

tnedutS A B C D E F G H I J K L M

htaMkram

36 25 38 17 35 59 64 68 86 03 08 23 04

scisyhPkram

65 45 68 57 85 78 25 09 66 83 15 11 38

a) Draw a scatterplot of the points with Math

marks on the horizontal axis and draw the

line of best fit.

b) Does there appear to be a relationship

between the plotted points? Describe the

type of relation you believe is occurring.

c) Use your graph to predict a Physics mark

for student N if his/her Math mark is 75.

UNIT 1


DO AND SEND 2TOTAL POINTS: 20

UNIT 1 COURSE PROJECT

Do the following questions and send them to

your marker. The point value for each is at the

end of the question.

BACKGROUND INFORMATION:

You will begin working on a project in this unit

that will involve the use of skills and concepts

acquired in the previous lessons. This project

will continue in each unit to reinforce the topics

covered within that unit. The work in this unit

will be similar to the unit assignments. Send

them to your marker for evaluation.

THAM Incorporated is a Nova Scotia company.

THAM Inc. produces and markets various

mathematical instruments and computer

software. The products are used in business and

educational settings. Some of the items include

graphing calculators, math sets, computer

software for engineering and surveying

applications, and clinometers. THAM Inc. has

offices and retail outlets in Halifax, Moncton,

Montreal, Toronto, and Vancouver.

You have been recently hired by THAM Inc. as a

marketing consultant. Throughout this manual

you will investigate several relationships that exist

within THAM Inc. and extend your

mathematical knowledge at various intervals to

help solve problems presented to the corporation.

Your first assignment as marketing consultant is to

answer the following:

1. THAM Inc. is interested in monitoring the

sales of their graphing calculators. Like many

products there are times when sales rise and

when sales fall. Make a list of possible

independent variables which could affect the

number of graphing calculators sold

(dependent variable). 3 points

2. The table below shows the graphing calculator

sales for each month in the 2002 operating

year for each office.

htnoM xafilaH notcnoM laertnoM otnoroT revuocnaV

yraunaJ 24 04 36 89 59

yraurbeF 83 54 05 08 38

hcraM 05 05 06 87 09

lirpA 35 84 07 28 29

yaM 94 84 56 57 57

enuJ 26 56 28 69 001

yluJ 03 53 65 96 17

tsuguA 23 53 25 06 07

rebmetpeS 87 57 09 011 09

rebotcO 26 06 18 19 68

rebmevoN 85 94 27 87 87

rebmeceD 07 07 39 001 99

Which office appears to have the most

consistent sales? Explain how you derived

your answer. If a graph was used please

include it in your write-up. 8 points

MATHEMATICS 10


3. Does there appear to be any month(s) where

sales have increased significantly at all offices?

Explain why a sales increase may have

happened in these months. 2 points

4. Suppose you were given a sales report with 68

calculators sold in a month. The top of the

report is missing that gives the office location.

Which office is this report most likely from?

Explain? 2 points

5. THAM Inc. has just received an order for

1500 math sets. Their progress at the

Moncton office for the first week is shown.

syaDforebmuN steSforebmuNdetelpmoC

1 79

2 502

3 723

4 344

5 835

6 366

7 597

Use the data in the table to create a scatter plot

to show the relationship between the number

of days and the number of sets completed and

draw the line of best fit. 4 points

6. Using your graph, predict the number of days

to needed to fill the order. 1 point

ata management - correspondence studiescsp.ednet.ns.ca/documents/sample_lessons/grade_10/... ·...

Documents