18 LO4 Statistical Charts and Graphs

8/4/2019 18 LO4 Statistical Charts and Graphs

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Grade 12 Mathematical Literacy

LO4 Statistical charts and graphs: Scatter Plots, Lineof Best Fit

1. The degree of connection or association between two variables

can be described as positive correlation, strong negativecorrelation, zero correlation, etc.

1.1 Define the following correlations:

1.1.1 Negative correlation.

1.1.2 Perfect correlation.

1.1.3 Positive correlation.

1.1.4 Zero correlation.

1.2 Draw a scatter plot of each of the above correlations.

2. An ice hockey coach measured the height and weight of theeleven member of her team. He recorded the results in the tablebelow.

Person A B C D E F G H I J KHeight(cm): x

163 154 168 179 156 179 175 165 170 177 159

Weight(kg): y

57 56 59 65 60 70 68 58 54 66 62

2.1 Which is the independent variable?

2.2 Compare the weight and height of persons A and I.

2.3 Display the data above as a scatter plot.

Maths & Science Marketing


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3. The soccer coach compared the number of goals each of theplayers in the first and second teams scored during the season.She tabulated her results as follows:

POSITION GOALS SCORED:1st team GOALS SCORED:2ND team

Goalie 0 0

Sweeper 0 0

Left Half 1 0

Centre Half 0 0

Right Half 2 0

Left Link 1 2

Centre Link 1 3

Right Link 2 4

Left Wing 12 2Right Wind 19 5

Centre Forward 28 32

3.1 Show the above information on a scatter plot.

3.2 In your opinion, is there a correlationbetween the position played by a hockeyplayer and the number of goals scored?

3.3 Draw a line of best fit on your graph to seewhether it supports your answer to 3.2 above.

4. There appears to be a direct correlationbetween the price of a second hand motorvehicle and the mileage the motor vehiclehas done. The table on the right shows themileage and selling price of a number ofvehicles sold by Gilmore Motors.

4.1 Draw a scatter plot of the data in thetable.

4.2 How would you describe the patternformed by the points in this scatter plot.


SellingPrice (R)

Mileage(km)

180 000 10 000

160 000 20 000

140 000 30 000

120 000 40 000

100 000 50 000

90 000 55 000

70 000 60 000

50 000 70 000

45 000 80 000

40 000 85 000


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5. The Grade 12 Mathematical Literacy teacher compared the markher learners achieved in their Mathematical Literacy examinationto their mark they achieved in their English Grammar examination.The teacher listed the Mathematical Literacy mark and Englishmark as pairs of co-ordinates as follows:

5.1 Plot the points on a scatter plot.

5.2 Draw a line of best fit.

5.3 Determine the mean, mode and median for the MathematicalLiteracy examination results.


(35;45) (21;24) (70;68) (56;54) 78;79) (92;91)(77;81) (67;71) (67;67) (90;93) (80;82) (35;41)(44;46) (48;49) (56;65) (66;69) (78;81) (45;46)


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ANSWERS

1.1.1 Negative correlation: The points on a scatter plot lie more orless on a line with a negative gradient.

1.1.2 Perfect correlation: The points of the scatter plot lie perfectlyon a line, either with a positive or a negative gradient.

1.1.3 Positive correlation: The points of the scatter plot lie more ofless on a line with a positive gradient.

1.1.4 Zero correlation: The points of the scatter plot are notconnected in any way.

1.21.2.1 Negative correlation:

0

20

40

60

80

100

120

0 2 4 6 8 10 12



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1.2.2 Perfect correlation:

0

20

40

60

80

100

120

0 2 4 6 8 10 12

1.2.3 Positive correlation:

0

20

40

60

80

100

120

0 2 4 6 8 10 12

1.2.4 Zero correlation:

0

5

10

15

20

25

30

0 2 4 6 8 10



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2.1 Height is the independent variable, and weight is the dependentvariable.

2.2 A weights 57 kg and is 163 cm tall, while I weights 54 kg and is170 cm tall. From this information it is clear that you cannotdetermine a persons weight if you know the persons height.Different people have different metabolisms and bonestructures, which means that it is not possible to determine apersons weight based on their height.

2.3

Hockey team weight and height

0

10

20

30

40

50

60

70

80

150 160 170 180 190

Height in cm

Weightinkg

Hockey team weight and

height



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3.1

Number of goals scored

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Number of position played

Numberofgoalsscored

First team

Second team

3.2 There is a correlation between the position played and thenumber of goals scored. The players who play at the back ofthe field, such as the goalie, the sweeper and the halves, do notseem to score goals, but the players who play at the front of thefield such as the centre forward and the left and right wings,seem to score most of the goals.

3.3

Number of goals scored

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Number of position played

Numberofgoalsscored

First team

Second team

The line drawn on a scatter plot where there are an equalnumber of points above and below the line is the line of best fit,which reflects the trend shown by the scatter plot.



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4.1

Cost vs Mileage

0

20000

40000

60000

80000

100000

0 50000 100000 150000 200000

Selling Price

Mileage

Cost vs Mileage

4.2 There is a negative correlation between the selling price of amotor vehicle and the mileage of the motor vehicle. The higherthe mileage the lower the selling price of the vehicle.



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5.1

Marks for Mathematical Literacy and

English

0

20

40

60

80

100

0 5 10 15 20

Number of learners

Marksoutof10

Mathematical Literacy

Marks

English Marks

5.2

Marks for Mathematical Literacy and

English

0

20

40

60

80

100

0 5 10 15 20

Number of learners

Marksoutof1

Mathematical Literacy

Marks

English Marks

5.3 Mean:

dataofNo.

dataofSum3961

18

1105,=

Mode: 35; 56; 67; 78

Median:2

6766 += 66,5


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18 LO4 Statistical Charts and Graphs