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  • Level: GCSE
  • Subject: Maths
  • Word count: 10981

Are left-handed people more intelligent and creative than the right-handed in Mayfield High School?

Extracts from this document...

Introduction

:Bryan Yip 10R

Maths Coursework

Are left-handed people more intelligent and creative than the right-handed in Mayfield High School?

In my coursework, I am going to focus on the IQ, Key Stage 2 results, favourite colour, favourite subject and height of students in Mayfield High School.

Specify, I will concentrate on the Year 7,8 and 9 boys and girls because these year groups have closer relationship with the Key Stage 2 results.

In the following coursework I am going to investigate:

  1. Do left-handed people have a higher IQ than the right-handed?
  2. There is a correlation between the IQ and the Key Stage 2 results for the left-handed and the right handed.
  3. Red colour always gives people the feeling of aggressive. Creative people often have new ideas and are willing to try, so more left-handed people like “red” than right-handed.
  4. The subjects “ Design & Technology”, “Art” and “Music” always require

creativity. More left-handed people like these subjects.

Before selecting the data, I will stratify the data. Stratifying data can reflect all of the data in Mayfield College,

Number of Boys

Number of Girls

Total

Overall number of people in Mayfield College

414

398

812

% in school (cor. to the nearest integer)

50%

50%

100%

Stratifying the number of right-handed in Year 7, 8 and 9

Number of Boys

Number of Girls

Total

% of  certain year of boys in the total of the right-handed

% of  certain year of girls in the total of the right-handed

Year 7

133

108

241

21%

17%

Year 8

105

93

198

17%

15%

Year 9

94

99

193

15%

15%

I will take about 16% of the people in from Mayfield. 8% of the left-handed and 8% of the right-handed. Having the same amount of data can have fair results.

For the right-handed, I will have 38% of them from Year 7 and 21% from boys and 17% from the girls. That means for my collected data, I should have 60x 21% from boys and 60x 17% from girls. I will take 32% from Year 8, 17% are from the boys and 15% from the girls.

...read more.

Middle

112

49

12544

784

2

100

4

10000

200

6

102

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10404

612

2

109

4

11881

218

6

107

36

11449

642

5

100

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10000

500

5

102

25

10404

510

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106

16

11236

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5

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10404

510

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14400

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12321

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105

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11025

525

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107

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11449

428

2

113

4

12769

226

6

103

36

10609

618

4

102

16

10404

408

3

108

9

11664

324

6

107

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11449

642

6

100

36

10000

600

2

83

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6889

166

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10000

500

2

102

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10404

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2

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10000

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6

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36

11881

654

2

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10000

200

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10000

400

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25

13456

580

4

100

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103

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10609

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5

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10000

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107

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11449

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103

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10609

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88

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7744

352

5

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25

10000

500

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100

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10000

400

3

109

9

11881

327

4

103

16

10609

412

4

97

16

9409

388

5

103

25

10609

515

4

108

16

11664

432

5

103

25

10609

515

3

100

9

10000

300

4

100

16

10000

400

4

102

16

10404

408

4

106

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11236

424

5

120

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14400

600

3

112

9

12544

336

6

100

36

10000

600

Σy=253

Σx=6249

Σy²=1127

Σx²=65337

Σxy=26395

Formula for PMCC

Σ x Σ y  

 r = Σxy -                      n _____________            

     √ 〔 Σ x² -  ( Σ x )²〕〔 Σ y² -  ( Σ y )²

                          n                        n

Substitute all the numbers into the formula

(6249)(253)  

 r = 26395 -                      60 _____________            

     √ 〔 653327 -  ( 6249 )²〕〔 1127-  ( 253 )²

  1. 60

 r = 26395 -                     26349.95_____________            

     √ 〔 653327 –650833.35〕〔 1127-1066.816667〕

r = 45.05_______________________            

     √〔2493.65〕〔 60.183333〕

r = 45.05_______________________            

     387.3966561

r=0.1163 (cor. to 4 d.p.)

The PMCC for the left-handed in IQ and English KS2 result is 0.1163. It’s a small positive correlation. It means there’s no big correlation between these two results. Next I am going to draw a scatter diagram to show the line of best fit, and show how the data are distributed.

image01.pngPick two points from the line of best fit, find the slope

(2, 101) and (5,103)

103-101

5-3

=0.67(cor. to 2 d.p.)

Extend the line of best fit and read out the y-intercept

y-intercept is 101

we have the y-intercept and the slope, so we can find the formula for the line of best fit.

y=mx+c

y=0.67x+101

Same as the one that we did before

Real x equals to the x co-ordinate of the data

Real y equals to the y co-ordinate of the data

y=0.67x+101 is the formula of the line of best fit

The difference between the co-ordinates of the data and the co-ordinate of the line of best fit is equal to Real y- line y

y2 is not to let the difference have a negative number.

Then we calculate the total of it to see how much difference between the real x and the line x.

Real x

Real y

y= 0.67 x + 101

Real y  - line y

y2

4

107

103.68

3.32

3.32

4

103

103.68

-0.68

0.68

4

112

103.68

8.32

8.32

4

100

103.68

-3.68

3.68

4

113

103.68

9.32

9.32

4

116

103.68

12.32

12.32

4

106

103.68

2.32

2.32

4

97

103.68

-6.68

6.68

7

112

105.69

6.31

6.31

2

100

102.34

-2.34

2.34

6

102

105.02

-3.02

3.02

2

109

102.34

6.66

6.66

6

107

105.02

1.98

1.98

5

100

104.35

-4.35

4.35

5

102

104.35

-2.35

2.35

4

106

103.68

2.32

2.32

5

99

104.35

-5.35

5.35

4

106

103.68

2.32

2.32

5

102

104.35

-2.35

2.35

4

120

103.68

16.32

16.32

4

111

103.68

7.32

7.32

5

100

104.35

-4.35

4.35

5

105

104.35

0.65

0.65

4

107

103.68

3.32

3.32

2

113

102.34

10.66

10.66

6

103

105.02

-2.02

2.02

4

102

103.68

-1.68

1.68

3

108

103.68

4.32

4.32

6

107

105.02

1.98

1.98

6

100

105.02

-5.02

5.02

2

83

102.34

-19.34

19.34

5

100

104.35

-4.35

4.35

2

102

102.34

-0.34

0.34

2

100

102.34

-2.34

2.34

6

109

105.02

3.98

3.98

2

100

103.01

-3.01

3.01

4

100

103.68

-3.68

3.68

5

116

104.35

11.65

11.65

4

100

103.68

-3.68

3.68

4

103

103.68

-0.68

0.68

5

100

104.35

-4.35

4.35

4

107

103.68

3.32

3.32

4

103

103.68

-0.68

0.68

5

100

104.35

-4.35

4.35

4

88

103.68

-15.68

15.68

5

100

104.35

-4.35

4.35

4

100

103.68

-3.68

3.68

3

109

103.01

5.99

5.99

4

103

103.68

-0.68

0.68

4

97

103.68

-6.68

0.68

5

103

104.35

-1.35

1.35

4

108

103.68

4.32

4.32

5

103

104.35

-1.35

1.35

3

100

103.01

-3.01

3.01

4

100

103.68

-3.68

3.68

4

102

103.68

-1.68

1.68

4

106

103.68

2.32

2.32

5

120

104.35

15.65

15.65

3

112

103.01

8.99

8.99

6

100

105.02

-5.02

5.02

Total=287.81

The total difference between the co-ordinate of the data and the co-ordinate of the line of best fit is 287.81

Comparing the PMCC and scatter diagram between the left-handed and right-handed in the correlation of IQ and Key Stage two results

The PMCC for the right-handed is -0.00479 and the PMCC for the left-handed is 0.1163. Both of them have a low correlation. Obviously, the left-handed have a higher low correlation between the English Key Stage result and the IQ.

After calculating the PMCC, we plotted the graph. In the graph, we can see that the data of the right-handed is more spread out than the left-handed, we can prove that by calculating the differences between the co-ordinates on the line of best fit and the co-ordinates on that was given.

So in conclusion, there’s no big relationship between the English Key Stage 2 results and the IQ.

Then we are going to investigate if there’s a correlation between the Maths Key Stage 2 results and the IQ.

Formula for PMCC

Σ x Σ y  

 r = Σxy -                      n _____________            

     √ 〔 Σ x² -  ( Σ x )²〕〔 Σ y² -  ( Σ y )²

                          n                        n

I will find the PMCC of the Maths KS2 result to IQ of the left-handed and right-handed, then compare them.

First I am going to draw a table for right-handed, let x be the Key Stage 2 result and y be the IQ of the right-handed

x

y

x2

y 2

xy

4

101

16

10201

404

4

101

16

10201

404

4

97

16

9409

388

3

99

9

9801

297

4

109

16

11881

436

5

90

25

8100

450

4

100

16

10000

400

4

100

16

10000

400

4

101

16

10201

404

5

99

25

9801

495

4

108

16

11664

432

5

97

25

9409

485

4

100

16

10000

400

5

100

25

10000

500

5

104

25

10816

520

5

103

25

10609

515

5

101

25

10201

505

4

94

16

8836

376

4

94

16

8836

376

5

100

25

10000

500

4

107

16

11449

428

4

101

16

10201

404

5

106

25

11236

530

4

65

16

4225

260

...read more.

Conclusion

Aim 3:

Calculating the % of left-handed and right-handed, we can have a general idea of if more left-handed people like red or if more right-handed people like red.

Pie Chart can show the data even more obviously and clearly.

Aim 4:

Also by using % and Pie chart, the data is clearly shown in a general idea.

This has showed my original statements to be correct/incorrect because:

Aim 1:  The statement might be correct, because an important information that we collected was more than 75% of the left-handed have a higher IQ than the median of the right-handed. Overall the average of IQ of the left-handed is higher. And the range of the left-handed IQ is smaller because from lots of reliable graphs, the data is obvious.

Aim 2: From the scatter Diagram and the PMCC, we can say the second statement is incorrect, because when we calculate the PMCC, there’s only a very low positive correlation between the KS2 results and the IQ, so that means there isn’t a big correlation between the KS2 results and IQ. In the Scatter Diagram, we cant even see clearly what’s how the data is distributed, and I saw there’s no obvious correlation from the graph.

Aim 3: From the Pie chart and calculating the %, I can say the third  statement is totally wrong, because the % of left-handed who like red is far away from the right-handed. So I think the graphs and calculation make the statement to be incorrect.

Aim 4: In the investigation of if those creative subjects, we can more left-handed like these subjects than the right-handed. We can see that obviously from the Pie chart, so the Statement is correct.

I am happy that my conclusions are reliable :

Most of the extreme data is removed and the calculation is repeated more than once to check whether the answer is correct. Except for that, the data is stratified before taken, so it reflects the real situation in more realistic way.

...read more.

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