scatter plots as 12.4.2

8/4/2019 Scatter Plots as 12.4.2

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ScatterScatter

PlotsPlots

A S – 12.4.2



Scatter plots are used

for data sets in whichthere could to be somesort of patternbetween two different

variables.• Scatter plots are most useful whenthere

are a large number of points. Thesedatapoints are plotted but not joined.

• Points that do not fit the generaltrend isan outlier. Do not consider this pointwhen “looking” at trends.



Francois records how

many hours his friendsspent studying andthen records whathappens to their

marks.

hoursstudying %change

1 1

1 -12 2

3 1

3 54 3

6 2

5 4

It is not easy to see anypattern or trend.

e.g. one friend studied for1 hour and his markschanged by 1% whileanother friend also

studied for one hour and

An ExampleAn Example



hours

studying

%

change

1 1

1 -1

2 2

3 1

3 5

4 3

6 3

5 4

Graph this data.

1 2 3 4 5

Study hours

6

5

4

3

2

10

-1

%

change

What does Frans notice?

Points are scattered but they seem to be

getting higher as the number of hoursincrease.

DO NOT connect the dots.



1 2 3 4 5

Study hours

6

5

4

3

2

10

-1

%

change

This is called the line of best fit – It helpsto show the trend between the variables.

Now draw a

straight line thatruns as close aspossible throughthe middle of

the set of datapoints.

Using this line of best fit, suggestFrans’s % change in his mark if hestudied 2 hours.

1%

Use your ‘eye’ - try to get an equalno. of points on either side.Disregard outliers.



When a scatter plot shows an associationor trend between two variables there isnot necessarily a cause and effect

relationship. It is only a suggestion as both variablescould be related to some third variablethat actually causes the apparentassociation.

Associations

The relationshipbetween the variablescan be either positive,negative or have no

association.



Types of ScatterTypes of Scatter

PlotsPlots This plot couldshow anincrease in achild’s height astheir ageincreases.

This plot could

show an increasein a child’s massas their ageincreases.



Make asuggestion asto what eachscatter plotcould show.

T o d o



Which graph most likely represents the followin

• The height of boys and the size of shirts worn by them.

• The temperature and the amount of gasneeded

to heat a house on a day.

• The size of shoes of adults

x

y

x x x

xxx

x

Graph A

x

y

x x x

x xx

x

Graph B

x

y

x

x

x

xxx x

Graph C

Graph A

Graph C

Graph B



TVhours

Grade%

12 70

10 85

5 823 88

15 65

16 75

8 68

A survey of randomly selected learnerscompared the no. of hours of TV they

watchedper week with their grade averages.

Create a scatter plot for thisdata.

100

80

60

40

20

0

TV hours0 4 8 12 16

Gra

de%

Let’s PlotLet’s Plot



100

80

60

40

20

00 4 8 12 16

Can you make anysuggestions aboutthe effect that

watching TV has onacademicachievement?

Classify the linear association.Draw a line of best fit.

Weak negative

The more TV you watch the greater

the chance of a decrease in

Use this line to determine your grade % if you watch 8 hours of TV.

80 hours

Grad

e%

TV hours



0 1 2 3 4 5 6 7

90

80

7060

50

40

30

20

10

0Age in year

Price

(R

)i n

thousa

nds

This scatter plotshows the selling

price of secondhand cars of thesame model.One car isadvertised

wrongly. Give theage and price.6 years, R72 000

What type of association is this?Strongly negative

A 4-year old car has to be

advertised. What price should it ≈ R55 000



A consumer group collected thefollowing data on the relationship

between the mass of a car and itsaverage consumption in ℓ /100km.Mass(kg)

ℓ per100km

1250 5

1420 7,6

950 4,2

1850 61220 6,8

1650 7,2

1010 6

Create a scatter plot for thisdata.

0 400 800 1200 1600 2000

mass(kg)

12

108

6

42

0ℓper

100k

m



0 400 800 1200 1600 20mass(kg)

ℓ

per1

00k

m

12

10

86

4

2

0

Circle the outlier.

Predict the mass if the car uses8ℓ 100km. 1800kg

What type of association isthis?

Circle the car that

travels the furtheston 50ℓ of petrol.

Strong positive

What does the

graph tell us aboutthe mass of thecar and theconsumption?

The greater the mass, the greater the consumpti



ww

w.rand

-forex.co.za

Is the Dollar stronger

or weaker if the Dollarper Euro rateincreases?

The scatter plotshows the relationship

between the Dollarper Euro and the goldprice in 2004.

What does the line of best fit tell us about therelationship between the Dollar, Euro and goldprice.

The gold price is increasing while

the dollar is weakening against

Weaker

scatter plots as 12.4.2

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