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Comparing Left-Handed and Right-Handed People

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Comparing Left-Handed and Right-Handed People

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. In my
collected data, I should have 60x 17% boys and 60x 15% from girls. In
Year 9, I will take 15% from boys and 15% from girls, so

In the following table, I am going to calculate what the actual number
of data that I am going to get

Number of Boys should be chosen in my data

Number of girls should be chosen in my data

Year 7

60x21%=13

60x17%=10

Year 8

60x 17%=10

60x 15%=9

Year 9

60x 15%=9

60x 15%=9

In total there be 60 data from the right-handed.

Stratifying the left-handed people in year 7,8 and 9

Number of Boys

Number of girls

Total

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

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

Year 7

16

21

37

10%

13%

Year 8

36

29

65

23%

18%

Year 9

20

36

56

13%

23%

=158

I will take 60 data from the left-handed people

Number of Boys should be chosen in my data

Number of girls should be chosen in my data

Year 7

60x10%=6

60x13%=8

Year 8

60x 23%=14

60x 18%=10

Year 9

60x 13%=8

60x 23%=14

In Total, there will be 60 left-handed data

I will have to collect to collect the following information

Aim 1: 60 IQ of the left-handed and 60 IQ of the right-handed

in Year 7,8 and 9.


Aim 2: 60 people of the IQ of the left-handed and 60 people of the IQ
of the right-handed.
---------------------------------------------------------------------

Key Stage results [English] [Maths] [Science] of the left-handed and
the

right-handed in Year 7, 8 and 9.

Aim 3: Collect 60 people who likes red in Year 7, 8 and 9.

Aim 4: Collect 20 people who like Design & Technology

20 people who like Art

20 people who like Music


I know this data s reliable because
-----------------------------------

Before choosing the data, I have already excluded the missing data and
the extreme data. All of these data are randomly chosen.

For all data, I chose Year 7, 8 and 9 because these years are closer
to their KS2 results.

This can make the KS2 results more reliable, so in Aim 2 the answer
might be more accurate.


I will use a sample of size
---------------------------

Aim 1: 60 people of the IQ of the left-handed and 60 people of the IQ
of the right-handed.


Aim 2: 60 people of the IQ of the left-handed and 60 people of the IQ
of the right-handed. Key Stage results [English] [Maths] [Science] of
the left-handed and the right-handed in Year 7, 8 and 9.
---------------------------------------------------------------------

Aim 3: 60 people who likes red in Year 7, 8 and 9.

Aim 4: 20 of people who like Design & Technology

20 of people who like Art

20 of people who like Music


I will make sure that my sample is fair
---------------------------------------

-Exclude all the missing and anonymous data before choosing them.

-By having the same amount of data of the left-handed and the
right-handed.


I will use this data to compare
-------------------------------

Aim 1: Comparing the mean of the IQ of the left-handed people and the
IQ of the right-handed people. As if the IQ of the left-handed people
has a higher IQ then I can say they are more intelligent.

Aim 2: Comparing the correlation of the IQ and the Key Stage 2 results
of the left-handed and the right-handed.

Aim 3: Calculating the percentages of left-handed and right-handed who
likes red and find out the answer.

Aim 4: Comparing in the "Creative Subjects", do more left-handed
people take these subjects than the right-handed? By calculating the
percentage of left-handed and right-handed people who take these
subjects, we can find out the answer.

I will perform the following calculations:

Aim 1: Do a Cumulative Frequency table and divide data into groups

Calculate the median of the IQ of the left-handed and the median of
the IQ

of the right-handed

Calculate the Upper Quartile and the Lower Quartile of the Data.

Calculate the IQR of both left-handed and right-handed

Compare the IQR of the IQ of the left-handed and the right-handed, to
see how their data is spread and to see how much the data is
concentrated about the median.

Do another table for left-handed. Calculate the frequency density. In
this table, the class interval will be different.

Calculate the mean and standard deviation, to find out the average of
the IQ of the left-handed and the right-handed, see who is clever and
by calculating the Standard deviation, we can find whether the data is
concentrated with the mean or not.

Aim 2: By Calculating the PMCC of the English result and the IQ

the PMCC of the Maths result and the IQ

the PMCC of the Science result and the IQ

to see if these results are high, low, positive or negative
correlated.

Aim 3: Get 60 data of students who like "red"

Then work out how many of them is left-handed and right-handed. Find
the percentage of the left-handed and right-handed that likes red.

Aim 4: Get 60 data of students who like studying "creative subjects"

Then find out how many students who like these subjects are
left-handed and right-handed. Work out the percentage of how many of
them is left-handed or right-handed.

These calculations will be useful because:

Aim 1: In this aim, I calculated the IQR because it can tell me
clearly about how much the data is spread about the median. IQR is not
affected by extreme data, so it won't affect the accuracy of the
range.

Except for IQR, I calculated S.D. and mean. Standard Deviation shows
how the data is spread from the mean. We can show that left-handed is
cleverer than the right-handed directly by mean and the S.D. can help
to show how the data is spread away from the mean.

Aim 2: PMCC can show the data if it's high/low, positive/negative
correlated. It shows if there's a relationship between the KS2 results
and the IQ.

Aim 3 & 4: In these two aims, I calculate things in percentage. It can
show results clearly.

I will check that the calculations make sense by:

Calculating the answer twice, to see if I get the same answer. If the
answer is correct, that means I am right

In the Aim 2, the answers of PMCC must lie between 1 and -1, so if the
answers of the PMCC lie between 1 and -1, it means the answers are
correct.

I will show the information in the following types of diagrams:

Aim 1: Cumulative Frequency Curve will be used.

Then I can find the median, Upper Quartile Range and Lower Quartile
Range

Box & Whisker diagram will be used. In comparing two data, we use the
same scale in the Box & Whisker diagram and it can help to express how
the data is spread.

Draw histogram for the IQ of the left-handed and right-handed. Then
compare the diagrams

Aim 2: scatter diagram can be used to show if the data is high/low,
positive/negative correlated.

Aim 3&4: Pie Charts are efficient to show the percentage of
left-handed people and right-handed people who like "red" or "creative
subjects"

As a result of the calculations and diagrams I will be able to
compare:

Aim 1: Compare the IQR and median

S.D. and mean of the left-handed and the right-handed

Aim 2: Compare the PMCC and correlation of the left-handed and the
right-handed, calculate which one has a higher correlation. high/low,
positive/negative correlated.

Aim 3:Compare the percentage of people who like "red"

Aim 4:Compare the percentage of people who like studying "creative
subjects"

Calculation


Aim 1:

First I will plot a table and divide all the IQ of the left-handed and
right-handed into different group and I can calculate the Cumulative
Frequency.

Right-handed

Class Interval of IQ

Frequency

Cumulative Frequency

0-10

0

0

10-20

0

0

20-30

0

0

30-40

0

0

40-50

0

0

50-60

0

0

60-70

2

2

70-80

1

3

80-90

6

9

90-100

24

33

100-110

23

56

110-120

3

59

120-130

1

60

Left-handed

Class Interval of IQ

Frequency

Cumulative Frequency

0-10

0

0

10-20

0

0

20-30

0

0

30-40

0

0

40-50

0

0

50-60

0

0

60-70

0

0

70-80

0

0

80-90

2

2

90-100

20

22

100-110

28

50

110-120

10

60

120-130

0

60

In the first graph, Cumulative Frequency Curve of the IQ of the
Right-handed

I found the Lower Quartile

the Upper Quartile

the Interquartile Range

the Median of the right-handed

Lower Quartile: In total, there are 60 data. To find the LQ, we must
calculate 60 x 25%=15, then cross the y-axis from 15 till it meets the
curve. When it meets the curve, vertical down till it meets the
x-axis. Read the x-intercept, and that's the LQ.

Upper Quartile: There are 60 data in total, to find the UQ, calculate
60x75% =45. Cross the y-axis from 45 till it meets the curve. When it
meets the curve, vertical down till it meets the x-axis. Read the
x-intercept and that's the UQ.

Lower Quartile= 92 Upper Quartile= 105

Interquartile Range= 105 - 92=13

Median= 98

In the second graph, Cumulative Frequency Curve of the IQ of the
Left-handed

I found the Lower Quartile

the Upper Quartile

the Interquartile Range

the Median of the left-handed

Lower Quartile = 100 Upper Quartile= 108

Interquartile Range= 108 - 100= 8

Median= 102

With these results, I can compare the median, upper quartile, lower
quartile, maximum and minimum data of the left-handed and right-handed
by Box and Whisker diagram

From the comparing of the Box and Whisker Diagram of the left-handed
and the right-handed

We can comment:

Ÿ Both of them have a positive skew, but the left-handed have a have a
higher positive skew than the right-handed. The skew of the
right-handed is almost medium, but it is still a positive skew. The
skew of the left-handed is showed clearly, we can classify it as a
positive skew easily.

Ÿ From the left-handed and right-handed box and whisker diagram, both
of them are positive skew, so they have higher mean than median

Ÿ The range and IQR of right-handed IQ is bigger than the left-handed
IQ.

That shows the range of the left-handed IQ is much more concentrated
and the data is not spread out widely.

Ÿ More than 75% of the left-handed IQ is higher than the median IQ of
the right-handed.

Histogram is useful to see how the data is distributed, so I am going
to draw histogram to show how data is spread.

First we have to draw another tables of the left-handed IQ and the
right-handed IQ to calculate the frequency density. Then we can start
to draw the two histograms. One for the left-handed and one for the
right-handed.

Frequency Density= Frequency / Class interval

Left-handed IQ

Class Interval

Frequency

Frequency Density

0-80

8

3

0.4

80-90

1

6

6

90-100

1

24

24

100-110

1

28

28

110-130

2

10

5

Right-handed IQ

Class Interval

Frequency

Frequency Density

0-80

8

0

0

80-90

1

2

2

90-100

1

20

20

100-110

1

28

28

110-130

2

10

5

After looking into the histograms of the left-handed and the
right-handed

I can comment:

Ÿ Both of the left-handed and the right-handed are concentrated in the
IQ range 90-100 and 100-110

Ÿ The data in the left-handed is more concentrated in 100-100 then the
right- handed , The Overall data for the right-handed is more spread
out than the left-handed.

Ÿ The overall distribution after left-handed is more concentrated than
the right-handed.

After looking into the histogram

We will try to investigate the data by mean and standard deviation. We
can use the standard deviation to compare the range of the left-handed
and the right-handed. See whether which is more spread out and compare
the mean of the IQ of the left-handed and right-handed. Find out if
the right-handed or left-handed has a higher average.

Formula to calculate the Mean

Formula for Mean:

∑ xn

n

Formula for Standard Deviation:

∑ represents the sum of a set of values

x represent the given data

_

x represent the mean

n is the number of value

First calculate the mean of the IQ of the right-handed

Mean:

∑ xn

n

IQ

101

65

101

69

101

71

101

87

101

88

101

90

102

90

103

90

103

90

103

91

104

92

104

94

104

94

105

97

105

97

105

98

106

98

107

98

107

99

108

99

109

99

116

100

116

100

116

100

122

100

100

100

100

100

100

100

100

100

101

101

Add all the numbers together, then divided by the n( that means the
number of value)

∑ xn

n

= 5949

60

=99.15

The mean of the right-handed is 99.15


Standard deviation of the IQ of the right-handed
------------------------------------------------

The x value in the formula

65

100

69

100

71

100

87

101

88

101

90

101

90

101

90

101

90

101

91

101

92

101

94

102

94

103

97

103

97

103

98

104

98

104

98

104

99

105

99

105

99

105

100

106

100

107

100

107

100

108

100

109

100

116

100

116

100

116

100

122

The x2 value in the data

4225

10000

4761

10000

5041

10000

7569

10201

7744

10201

8100

10201

8100

10201

8100

10201

8100

10201

8281

10201

8464

10201

8836

10404

8836

10609

9409

10609

9409

10609

9604

10816

9604

10816

9604

10816

9801

11025

9801

11025

9801

11025

10000

11236

10000

11449

10000

11449

10000

11664

10000

11881

10000

13456

10000

13456

10000

13456

10000

14884

In the formula of standard deviation

∑x2 = the sum of all the square of above data

= 595483

then in ∑x2

n

n= number of values =60

∴ ∑x2 = 595483 =9924.716667

n 60

The mean of the data that wasn't squared

= 99.15

_ 2

so x =( 99.15 )2 = 9830.7225

in the formula

we can substitute all the data and find the S.D. of the IQ of the
right-handed

_____________________

√9924.716667 - 9830.7225

_________

=√93.99416666

=9.6595058879

After calculating the Standard Deviation of the IQ of the right-handed

I will calculate the Mean and Standard Deviation of the IQ of the
right-handed

IQ of the left-handed:

83

100

107

88

100

107

97

102

107

97

102

107

99

102

107

100

102

108

100

102

108

100

102

109

100

103

109

100

103

109

100

103

111

100

103

112

100

103

112

100

103

112

100

103

113

100

105

113

100

106

116

100

106

116

100

106

120

100

106

120

Mean: Add all the above data together and divided by the number of
values

∑ xn

n

= 6249

60

=104.15

Then calculate the Standard Deviation

The x-values of the formula

83

100

107

88

100

107

97

102

107

97

102

107

99

102

107

100

102

108

100

102

108

100

102

109

100

103

109

100

103

109

100

103

111

100

103

112

100

103

112

100

103

112

100

103

113

100

105

113

100

106

116

100

106

116

100

106

120

100

106

120

Square all these data and find the x2 values in the formula

The data that were squared

6889

10000

11449

7744

10000

11449

9409

10404

11449

9409

10404

11449

9801

10404

11449

10000

10404

11664

10000

10404

11664

10000

10404

11881

10000

10609

11881

10000

10609

11881

10000

10609

12321

10000

10609

12544

10000

10609

12544

10000

10609

12544

10000

10609

12769

10000

11025

12769

10000

11236

13456

10000

11236

13456

10000

11236

19600

10000

11236

19600

Then add them all up to find the value ∑x2 in the formula

∑x2

= 663727

_

The x value means the mean of the data that wasn't squared

Mean =104.15

_

(x)2

=(104.15)2

=10847.2225

I have chosen 60 data only, so in this formula, the n (the number of
values) will be 60

Substitute all the numbers I have got into the formula

∑x2

n

663727

= 60

=11062.1167

_

(x)2

=10847.2225

_

∑x2 - (x)2

n

= 11062.1167-10862.1167

=200

Square Root 200 to find the standard deviation

√200

=14.14213562

The standard deviation for IQ of the left-handed

IQ of Left-handed

IQ of Right-handed

S.D.

14.14213562

9.6595058879

Mean

104.15

99.15

In the comparing of the Standard Deviation, we can see the S.D. of the
IQ of the Left-handed is obviously than the right-handed. The higher
the standard deviation, that means the higher the data is spread.
These results show the data of the left-handed spread wider than the
right-handed since the S.D. of the left-handed is higher than the
right-handed.

Then we compare the mean of the left-handed and the right-handed. The
left-handed have a higher mean than the right-handed. I can conclude
that the overall average of the IQ of the left-handed is higher than
the right-handed. The IQ of the left-handed is 104.15 and the IQ of
the right-handed is 99.15. The left-handed in average, have about 5 IQ
higher than the right-handed. Only 60 data is collected, so I can say,
the IQ that the left-handed are higher than the right-handed is 60 x
5=300 in the overall data, and in comparing the left-handed and the
right-handed IQ individually, form the data, I can say each left-hand
has 5 IQ higher than the right-handed, but we cant really say that
since different people have different IQ, but that's just a roughly
calculation.

After that I compare the IQR and the S.D. since they are both
calculating how the data spread out.

IQ

Left-handed

Right-handed

S.D.

14.14213562

9.659505887

IQR

8

13

The IQR of the IQ right-handed is 62.5% higher than the IQ of the
left-handed.

That means the data is more spread out in the right-handed

But the S.D. of the IQ of the left-handed is 46% higher than the
right-handed.

It shows the data in the left-handed is more spread out.

In the S.D. and IQR, both of them have different conclusion. But the
S.D. include all the small extreme data in it s even though I have
excluded the main extreme data, so the range is smaller than the
right-handed in the S.D., I think the IQR should be more trustable
since it has excluded all the extreme data.

Final Conclusion

From the Box and Whisker diagram and calculating the IQR, I can
conclude that the range of the IQ of the right-handed is spread wider
than the left-handed, since it has a higher IQR. In the Box and
Whisker diagram, both of them have a positive skew, that means the
data the left-handed and the right-handed are having, are higher than
the median. Also from the box and whisker diagram, it shows that more
than 75% of the IQ of the left-handed is higher than the IQ of the
right-handed median.

From comparing the histograms of the left-handed and right-handed, I
can say most of the IQ of both left-handed and right-handed are
concentrated between the range 100-120 and the data of the left-handed
is even more concentrated than the right-handed between the range
100-110.

In the calculation of standard deviation and mean, I found out the
mean of the left-handed is higher than the right-handed, it shows the
average of the left-handed is higher. Overall it reflects the IQ of
the left-handed is higher than the right-handed practically.

The reason that I didn't compare the range of the standard deviation
since it may contains some small extreme data, so the result was the
left-handed data is more spread out than the right-handed.

Aim 2:

Is there a correlation between the IQ and the Key Stage 2 results for
the left-handed and the right handed?

In the investigation of this aim, I am going to do 6 calculations

1) Correlation of the right-handed

-The English Key Stage results to the IQ

-The Maths Key Stage results to the IQ

-The Science Key Stage results to the IQ

2) Correlation of the right-handed

-The English Key Stage results to the IQ

-The Maths Key Stage results to the IQ

-The Science Key Stage results to the IQ

Then I will compare :

1) Correlation of the English Key Stage results to the IQ of
left-handed to right-handed

2) Correlation of the Maths Key Stage results to the IQ of left-handed
to right-handed

3) Correlation of the Science Key Stage results to the IQ of
left-handed to right-handed

I will calculate the correlation by using PMCC and scatter diagram

The answers for PMCC must lie between -1 to 1

-1 means high negative correlation

1 means high positive correlation

0 means there is no correlation

The closer the number to 0, the lower the correlation

Formula for PMCC

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

x represent the first kind of data (IQ)

y represent the second kind of data (KS2 results)

n represent the number of values

r is the PMCC

∑ represents the sum of a set of values

1) Calculate PMCC of the right-handed IQ to the English Key Stage
result

x

y

x2

y2

xy

101

4

10201

16

404

101

3

10201

9

303

97

5

9409

25

485

99

5

9801

25

495

109

4

11881

16

436

90

5

8100

25

450

100

4

10000

16

400

100

4

10000

16

400

101

4

10201

16

404

99

4

9801

16

495

108

3

11664

9

324

97

3

9409

9

291

100

5

10000

25

500

100

4

10000

16

400

104

4

10816

16

416

103

4

10609

16

412

101

4

10201

16

404

94

3

8836

9

282

94

5

8836

25

470

100

4

10000

16

400

107

3

11449

9

321

101

4

10201

16

404

106

4

11236

16

424

65

4

4225

16

260

100

5

10000

25

500

100

5

10000

25

500

103

5

10609

25

515

100

3

10000

9

300

71

5

5041

25

355

100

3

10000

9

300

98

4

9604

16

392

98

4

9604

16

392

104

5

10816

25

520

116

3

13456

9

348

105

5

11025

25

525

98

4

9604

16

392

104

5

10816

25

520

99

5

9801

25

495

100

4

10000

16

400

90

5

8100

25

450

88

3

7744

9

264

101

4

10201

16

404

116

5

13456

25

580

90

3

8100

9

270

107

4

11449

16

428

101

4

10201

16

404

92

4

8464

16

368

103

4

10609

16

412

116

5

13456

25

580

105

4

11025

16

420

90

3

8100

9

270

69

5

4761

25

345

102

4

10404

16

408

101

4

10201

16

404

100

3

10000

9

300

91

4

8281

16

364

122

5

14884

25

610

87

4

7569

16

348

100

5

10000

25

500

105

5

11025

25

525

Σx=5949

Σy=246

Σx²=595483

Σy²=1056

Σxy=24383

Substitute them into the formula

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

5949 x 246

r = 24383 - 60_____________

√ 〔 595483 - ( 5949)²〕〔 1056 - ( 248 )²〕

60 60

1463103.

r = 24383- 60_____________

√ 〔 595483 - 35390601〕〔 1056 - 61504〕

60 60

r= 24383 - 24385_______

√ 〔5639.65〕〔 30.93333334〕

r= -2___

417.6759191

r= -0.00479

Aftercalculation, the PMCC for the right-handed IQ to the English Key
Stage results is

-0.00479, which means it's a negative low correlation.

To show how the data is distributed, we can draw a scatter diagram

[IMAGE]


In this diagram, it shows there isn't any obvious correlation, and I
plot the line of best fit for my data. From the line of best fit, I
can calculate the equation for the line of best fit.

Pick two points from the line of best fit then find the slope of it

I picked (3,100) and (5, 99)

Slope:

100-99

8-3

=0.2

Extend the line of best fit to till it meets the y-intercept

Then read out the number, we can find the y-intercept

And the y-intercept is 99

So I can calculate the formula for the line

y=mx+c

y= -0.2(x) +99

From the line of best fit and the formula that I have just found out,
I can even see how much each point is away from the y in the line of
best fit.

In the bellowing box, real x means the x-coordinate that is plotted on
the graph

Real y means the y means the y-coordinate that is plotted on the graph

The third column y= -0.2 x + 99, is the equation that I have found,
which y equals the y-coordinate on the line of best fit and x equals
to the x-coordinate of the line of best fit.

The forth column Real y- line y, then see the difference the y
co-ordinate in the line of best fit and y-coordinate that I have
plotted on the graph

Real x

Real y

y= -0.2 x + 99

Real y - line y

√y2

4

101

98.2

2.8

2.8

3

101

98.4

2.6

2.6

5

97

98

-1

1

5

99

98

1

1

4

109

98.2

10.2

10.2

5

90

98

-8

-8

4

100

98.2

1.8

1.8

4

100

98.2

1.8

1.8

4

101

98.2

2.8

2.8

4

99

98.2

0.8

0.8

3

108

98.4

9.6

9.6

3

97

98.4

-1.4

1.4

5

100

98

2

2

4

100

98.2

1.8

1.8

4

104

98.2

5.8

5.8

4

103

98.2

4.8

4.8

4

101

98.2

2.8

2.8

3

94

98.4

-4.4

4.4

5

94

98

-4

4

4

100

98.2

1.8

1.8

3

107

98.4

8.6

8.6

4

101

98.2

2.8

2.8

4

106

98.2

7.8

7.8

4

65

98.2

-33.2

33.2

5

100

98

2

2

5

100

98

2

2

5

103

98

5

5

3

100

98.4

1.6

1.6

5

71

98

-27

27

3

100

98.4

1.6

1.6

4

98

98.2

-0.2

0.2

4

98

98.2

-0.2

0.2

5

104

98

6

6

3

116

98.4

17.6

17.6

5

105

98

7

7

4

98

98.2

-0.2

0.2

5

104

98

6

6

5

99

98

1

1

4

100

98.2

1.8

1.8

5

90

98

-8

8

3

88

98.4

-10.4

10.4

4

101

98.2

2.8

2.8

5

116

98

18

18

3

90

98.4

-8.4

8.4

4

107

98.2

8.8

8.8

4

101

98.2

2.8

2.8

4

92

98.2

-6.2

6.2

4

103

98.2

4.8

4.8

5

116

98

18

18

4

105

98.2

6.8

6.8

3

90

98.4

-8.4

8.4

5

69

98

-29

29

4

102

98.2

3.8

3.8

4

101

107

1.2

1.2

3

100

98.4

1.6

1.6

4

91

98.2

-7.2

4.2

5

122

98

24

24

4

87

98.2

-11.2

11.2

5

100

98

2

2

5

105

98

7

7

Total=374.2

So the total number that difference between the co-ordinate of the
data and the co-ordinate of the line of best fit is 374.2

Now we investigate the correlation between the left-handed IQ and
English KS2 result by the same method.

In the following table, which means x is the IQ, y is the KS2 English
result of the left-handed

x

y

x2

y 2

xy

4

107

16

11449

428

4

103

16

10609

412

4

112

16

12544

448

4

100

16

10000

400

4

113

16

12769

452

4

116

16

13456

464

4

106

16

11236

424

4

97

16

9409

388

7

112

49

12544

784

2

100

4

10000

200

6

102

16

10404

612

2

109

4

11881

218

6

107

36

11449

642

5

100

25

10000

500

5

102

25

10404

510

4

106

16

11236

424

5

99

25

9801

495

4

106

16

11236

424

5

102

25

10404

510

4

120

16

14400

480

4

111

16

12321

444

5

100

25

10000

500

5

105

25

11025

525

4

107

16

11449

428

2

113

4

12769

226

6

103

36

10609

618

4

102

16

10404

408

3

108

9

11664

324

6

107

36

11449

642

6

100

36

10000

600

2

83

4

6889

166

5

100

25

10000

500

2

102

4

10404

204

2

100

4

10000

200

6

109

36

11881

654

2

100

4

10000

200

4

100

16

10000

400

5

116

25

13456

580

4

100

16

10000

400

4

103

16

10609

412

5

100

25

10000

500

4

107

16

11449

428

4

103

16

10609

412

5

100

25

10000

500

4

88

16

7744

352

5

100

25

10000

500

4

100

16

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

16

11236

424

5

120

25

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

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

Substitute all the numbers into the formula

(6249)(253)

r = 26395 - 60 _____________

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

60 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.

[IMAGE]Pick 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

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )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

4

100

16

10000

400

5

100

25

10000

500

5

103

25

10609

515

5

100

25

10000

500

4

71

16

5041

284

4

100

16

10000

400

3

98

9

9604

294

4

98

16

9604

392

4

104

16

10816

416

4

116

16

13456

464

3

105

9

11025

315

4

98

16

9604

392

4

104

16

10816

416

4

99

16

9801

396

3

100

9

10000

300

4

90

16

8100

360

5

88

25

7744

440

5

101

25

10201

505

5

116

25

13456

580

4

90

16

8100

360

4

107

16

11449

428

5

101

25

10201

505

3

92

9

8464

276

4

103

16

10609

412

5

116

25

13456

580

4

105

16

11025

420

4

90

16

8100

360

3

69

9

4761

207

5

102

25

10404

510

3

101

9

10201

303

5

100

25

10000

500

4

91

16

8281

364

3

122

9

14884

366

5

87

25

7569

435

3

100

9

10000

300

4

105

16

11025

420

Σx=251

Σy=5949

Σx²=1077

Σy²=595483

Σxy=24924

Substitute the collected data into the formula

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

251(5949)

r = 24924 - 60 _____________

√ 〔 1077 - ( 251 )²〕〔 595483 - ( 5949 )²〕

60 60

r = 37.35_____________

√ 〔 26.98333334〕〔5639.65〕

r = 37.35_____________

390.0981362

r = 0.0957( cor. to 4 d.p.)

The PMCC is 0.0957. It's a low positive correlation.

Then I am going to plot a scatter diagram to draw the line of best fit
and find the formula for it. Scatter Diagram can also show how the
data is spread.

[IMAGE]

From the graph, we can see the data is widely spread, that's why it's
a low positive correlation.

After drawing the line of best fit, I can calculate the equation for
the line.

Pick two points from the line of best fit and calculate the slope of
it

(3,100) (4, 103)

Slope:

103-100

4-3

=3

Extend the line of best fit till it meets the y-intercept

Then read out the number, we can find the y-intercept

And the y-intercept is 94

The formula of the line:

y=mx+c

y=3x+94

From the line of best fit and the formula that I have just found, I
can calculate how far each point is away from the line of best fit.

So next, I am going to plot a table, then find the number of the total
difference of all the points from the line of best fit.

In the following table, real x represents the x co-ordinate of the
points that wasn't on the line of best fit. Real y represents the y
co-ordinate of the points that wasn't on the line of best fit. With
the help of the formula that we have found, we can calculate the
answer.

Real x

Real y

y=3x+94

Real y - line y

√y2

4

101

106

-5

5

4

101

106

-5

5

4

97

106

-9

9

3

99

103

-4

4

4

109

106

3

3

5

90

109

-19

19

4

100

106

-6

6

4

100

106

-6

6

4

101

106

-5

5

5

99

109

-10

10

4

108

106

2

2

5

97

109

-12

12

4

100

106

-6

6

5

100

109

-9

9

5

104

109

-5

5

5

103

109

-6

6

5

101

109

-8

8

4

94

106

-12

12

4

94

106

-12

12

5

100

109

-9

9

4

107

106

1

1

4

101

106

-5

5

5

106

109

-3

3

4

65

106

-41

41

4

100

106

-6

6

5

100

109

-9

9

5

103

109

-6

6

5

100

109

-9

9

4

71

106

-35

35

4

100

106

-6

6

3

98

103

-5

5

4

98

106

-8

8

4

104

106

-2

2

4

116

106

10

10

3

105

103

2

2

4

98

106

-8

8

4

104

106

-2

2

4

99

106

-7

7

3

100

103

-3

3

4

90

106

-16

16

5

88

109

-21

21

5

101

109

-8

8

5

116

109

7

7

4

90

106

-16

16

4

107

106

1

1

5

101

109

-8

8

3

92

103

-11

11

4

103

106

-3

3

5

116

109

7

7

4

105

106

-1

1

4

90

106

-16

16

3

69

103

-34

34

5

102

109

-7

7

3

101

103

-2

2

5

100

109

-9

9

4

91

106

-15

15

3

122

103

19

19

5

87

109

-22

22

3

100

103

-3

3

4

105

106

-1

1

Total=548

So the total difference between the y co-ordinate of the data and the
y co-ordinate of the line of best fit is 548.

Next I will calculate the PMCC of left-handed and then compare it with
the right-handed

First draw a table

x

y

x2

y 2

xy

4

107

16

11449

428

3

103

9

10609

309

5

112

25

12544

560

5

100

25

10000

500

4

113

16

12769

452

5

116

25

13456

580

4

106

16

11236

424

4

97

16

9409

388

4

112

16

12544

448

4

100

16

10000

400

3

102

9

10404

306

3

109

9

11881

327

5

107

25

11449

535

4

100

16

10000

400

4

102

16

10404

408

4

106

16

11236

424

4

99

16

9801

396

3

106

9

11236

318

5

102

25

10404

510

4

120

16

14400

480

3

111

9

12321

333

4

100

16

10000

400

4

105

16

11025

420

4

107

16

11449

428

5

113

25

12769

565

5

103

25

10609

515

5

102

25

10404

510

3

108

9

11664

324

5

107

25

11449

535

3

100

9

10000

300

4

83

16

6889

332

4

100

16

10000

400

5

102

25

10404

510

3

100

9

10000

300

5

109

25

11881

545

4

100

16

10000

400

5

100

25

10000

500

5

116

25

13456

580

4

100

16

10000

400

5

103

25

10609

515

3

100

9

10000

300

4

107

16

11449

428

5

103

25

10609

515

3

100

9

10000

300

4

88

16

7744

352

4

100

16

10000

400

4

100

16

10000

400

4

109

16

11881

436

5

103

25

10609

515

4

97

16

9409

388

3

103

9

10609

309

5

108

25

11664

540

4

103

16

10609

412

4

100

16

10000

400

3

100

9

10000

300

4

102

16

10404

408

5

106

25

11236

530

4

120

16

14400

480

5

112

25

12544

560

5

100

25

10000

500

Σx=248

Σy=6249

Σx²=1056

Σy²=653327

Σxy=25878

Substitute all these data into the formula

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

248(6249)

r = 25878 - 60_____________

√ 〔1056 - ( 248)²〕〔 653327- ( 6249 )²〕

60 60

r = 48.8__________________________

√ 〔 30.93333334〕[ 2493.65 ]

r = 48.8_____________

277.7353177

r= 0.1757 (cor. To 4 d.p.)

The PMCC is 0.1757. It's a low positive correlation too.

Next, plot a scatter diagram to show how the data is spread and plot
the line of best fit then find the equation for it.

[IMAGE]

Equation for the line of best fit

Pick two co-ordinates from the line of best fit and calculate the
slope

(3, 101) (4, 103)

Slope:

103-101

4-3

=2

After the extension of line of best fit, the y-intercept is 99

Equation for the line of best fit

y=mx+c

y=2x+99

Plot another table to calculate the total number of the difference
between the real

y co-ordinate and the y co-ordinate on the line of best fit

Real x

Real y

y=2x+99

Real y - line y

√y2

4

107

107

0

0

3

103

105

-2

2

5

112

109

3

3

5

100

109

-9

9

4

113

107

6

6

5

116

109

7

7

4

106

107

-1

1

4

97

107

-10

10

4

112

107

5

5

4

100

107

-7

7

3

102

105

-3

3

3

109

105

4

4

5

107

109

-2

2

4

100

107

-7

7

4

102

107

-5

5

4

106

107

-1

1

4

99

107

-8

8

3

106

105

1

1

5

102

109

-7

7

4

120

107

13

13

3

111

105

6

6

4

100

107

-7

7

4

105

107

-2

2

4

107

107

0

0

5

113

109

4

4

5

103

109

-6

6

5

102

109

-7

7

3

108

105

3

3

5

107

109

-2

2

3

100

105

-5

5

4

83

107

-24

24

4

100

107

-7

7

5

102

109

-7

7

3

100

105

-5

5

5

109

109

0

0

4

100

107

-7

7

5

100

109

-9

9

5

116

109

7

7

4

100

107

-7

7

5

103

109

-6

6

3

100

105

-5

5

4

107

107

0

0

5

103

109

-6

6

3

100

105

-5

5

4

88

107

-19

19

4

100

107

-7

7

4

100

107

-7

7

4

109

107

2

2

5

103

109

-6

6

4

97

107

-10

10

3

103

105

-2

2

5

108

109

-1

1

4

103

107

-4

4

4

100

107

-7

7

3

100

105

-5

5

4

102

107

-5

5

5

106

109

-3

3

4

120

107

13

13

5

112

109

3

3

5

100

109

-9

9

Total=341

The total difference between the co-ordinate of the data and the
co-ordinate of the line of best fit is 341.

Comparing:

Right-handed

Left-handed

PMCC

0.0957

0.1757

Total of Real y-line y

548

341

Both of the PMCC of the left-handed and right-handed have a low
positive correlation, but the left-handed have a higher correlation,
that means the data is more concentrated and the data in the
right-handed is more spread out than the left-handed.

From the difference of the line of best fit and the total data, we can
it clearly that the data of the right-handed is more spread out than
the left-handed.

From the graph, the data of the left-handed is widely spread out than
the right-handed.

But also, because both of them don't have a high correlation in the
Maths KS2 results and the IQ, so IQ doesn't really affect the Maths
KS2 result.

Correlation between the IQ and the Science Key Stage Result of
left-handed and right-handed

Because in this aim, I am just repeating the same method but I will
use Science instead of Maths/English, so I won't repeat myself again
and not explaining the same thing again.

PMCC of left-handed

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

x

y

x2

y 2

xy

4

101

16

10201

404

4

101

16

10201

404

5

97

25

9409

485

4

99

16

9801

396

5

109

25

11881

545

5

90

25

8100

450

4

100

16

10000

400

5

100

25

10000

500

4

101

16

10201

404

3

99

9

9801

297

4

108

16

11664

432

4

97

16

9409

388

4

100

16

10000

400

4

100

16

10000

400

4

104

16

10816

416

4

103

16

10609

412

5

101

25

10201

505

3

94

9

8836

282

5

94

25

8836

470

5

100

25

10000

500

5

107

25

11449

535

4

101

16

10201

404

4

106

16

11236

424

4

65

16

4225

260

6

100

36

10000

600

5

100

25

10000

500

5

103

25

10609

515

3

100

9

10000

300

5

71

25

5041

355

5

100

25

10000

500

4

98

16

9604

392

5

98

25

9604

490

4

104

16

10816

416

3

116

9

13456

348

5

105

25

11025

525

4

98

16

9604

392

5

104

25

10816

520

4

99

16

9801

396

4

100

16

10000

400

5

90

25

8100

450

4

88

16

7744

352

4

101

16

10201

404

5

116

25

13456

580

3

90

9

8100

270

5

107

25

11449

535

4

101

16

10201

404

3

92

9

8464

276

4

103

16

10609

412

5

116

25

13456

580

5

105

25

11025

525

3

90

9

8100

270

5

69

25

4761

345

5

102

25

10404

510

4

101

16

10201

404

3

100

9

10000

300

4

91

16

8281

364

5

122

25

14884

610

4

87

16

7569

348

5

100

25

10000

500

5

105

25

11025

525

Σx=259

Σy=5949

Σx²=1149

Σy²=595483

Σxy=25726

Substitute these data into the formula

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

r = 25726 - 25679.85_____________

√ 〔1149 - ( 259)²〕〔595483 - ( 5949 )²〕

60 60

r = 46.15_____________________________

√ 〔30.98333334〕〔5639.65〕

r=46.15

418.0133441

r=0.1104 (cor. to 4 sig. Fig.)

Scatter Diagram

[IMAGE]


Slope: (4.100) (5,103)

103 - 100

5-4

slope = 3

y-intercept=96

equation for the line of best fit

y=3x +96

Real x

Real y

y=3x+96

Real y - line y

√y2

4

101

108

-7

7

4

101

108

-7

7

5

97

111

-14

14

4

99

108

-9

9

5

109

111

-2

2

5

90

111

-11

11

4

100

108

-8

8

5

100

111

-11

11

4

101

108

-7

7

3

99

105

-6

6

4

108

108

0

0

4

97

108

-11

11

4

100

108

-8

8

4

100

108

-8

8

4

104

108

-4

4

4

103

108

-5

5

5

101

111

-10

10

3

94

105

-11

11

5

94

111

-17

17

5

100

111

-11

11

5

107

111

-4

4

4

101

108

-7

7

4

106

108

-2

2

4

65

108

-43

43

6

100

114

-14

14

5

100

111

-11

11

5

103

111

-8

8

3

100

105

-5

5

5

71

111

-40

40

5

100

111

-11

11

4

98

108

-10

10

5

98

111

-13

13

4

104

108

-4

4

3

116

105

11

11

5

105

111

-6

6

4

98

108

-10

10

5

104

111

-7

7

4

99

108

-9

9

4

100

108

-8

8

5

90

111

-21

21

4

88

108

-20

20

4

101

108

-7

7

5

116

111

5

5

3

90

105

-15

15

5

107

111

-4

4

4

101

108

-7

7

3

92

105

-13

13

4

103

108

-5

5

5

116

111

5

5

5

105

111

-6

6

3

90

105

-15

15

5

69

111

-42

42

5

102

111

-9

9

4

101

108

-7

7

3

100

105

-5

5

4

91

108

-17

17

5

122

111

11

11

4

87

108

-21

21

5

100

111

-11

11

5

105

111

-6

6

Total=642

There is a low positive correlation between the Science Key Stage 2
result and the IQ, but the data of the results are spread out widely,
that means the low positive correlation is correct.

Calculate the PMCC for the left-handed

x

y

x2

y 2

xy

4

107

16

11449

428

4

103

16

10609

412

4

112

16

12544

448

5

100

25

10000

500

5

113

25

12769

565

5

116

25

13456

580

5

106

25

11236

530

4

97

16

9409

388

4

112

16

12544

448

5

100

25

10000

500

4

102

16

10404

408

5

109

25

11881

545

3

107

9

11449

321

4

100

16

10000

400

5

102

25

10404

510

5

106

25

11236

530

5

99

25

9801

495

4

106

16

11236

424

4

102

16

10404

408

5

120

25

14400

600

4

111

16

12321

444

5

100

25

10000

500

5

105

25

11025

525

4

107

16

11449

428

4

113

16

12769

452

4

103

16

10609

412

5

102

25

10404

510

5

108

25

11664

540

3

107

9

11449

321

4

100

16

10000

400

4

83

16

6889

332

5

100

25

10000

500

4

102

16

10404

408

4

100

16

10000

400

3

109

9

11881

327

4

100

16

10000

400

4

100

16

10000

400

5

116

25

13456

580

4

100

16

10000

400

5

103

25

10609

515

5

100

25

10000

500

4

107

16

11449

428

5

103

25

10609

515

5

100

25

10000

500

4

88

16

7744

352

5

100

25

10000

500

4

100

16

10000

400

4

109

16

11881

436

5

103

25

10609

515

4

97

16

9409

388

4

103

16

10609

412

4

108

16

11664

432

4

103

16

10609

412

3

100

9

10000

300

5

100

25

10000

500

4

102

16

10404

408

4

106

16

11236

424

5

120

25

14400

600

3

112

9

12544

336

6

100

36

10000

600

Σx=261

Σy=6249

Σx²=1161

Σy²=653327

Σxy=27192

PMCC

Σx Σy

r = Σxy - n _____________

√ 〔 Σ x² - ( Σx )²〕〔 Σy²- ( Σy )²〕

n n

r = 27192 - 27183.15_____________

√ 〔1161 - (261 )²〕〔 653327 - ( 6249 )²〕

60 60

r = 8.85____________ ________________

√ 〔 25.65〕〔2493.65〕

r= 8.85______

252.9073398

r=0.0350 (cor. To 4 d.p.)

This is a low positive correlation

Scatter Diagram

[IMAGE]

Slope: pick two points

(4,101)(5,102)

slope: 102-101

5-4

=1

y-intercept=101

Equation

y=1(x)+101

Real x

Real y

y=1x+101

Real y - line y

√y2

4

107

105

2

2

4

103

105

-2

2

4

112

105

7

7

5

100

106

-6

6

5

113

106

7

7

5

116

106

10

10

5

106

106

0

0

4

97

105

-8

8

4

112

105

7

7

5

100

106

6

6

4

102

105

-3

3

5

109

106

3

3

3

107

104

3

3

4

100

105

-5

5

5

102

106

-4

4

5

106

106

0

0

5

99

106

-7

7

4

106

105

1

1

4

102

105

-3

3

5

120

106

14

14

4

111

105

6

6

5

100

106

-6

6

5

105

106

1

1

4

107

105

2

2

4

113

105

-2

2

4

103

105

-2

2

5

102

106

-4

4

5

108

106

2

2

3

107

104

3

3

4

100

105

-5

5

4

83

105

-22

22

5

100

106

-6

6

4

102

105

-3

3

4

100

105

-5

5

3

109

104

5

5

4

100

105

-5

5

4

100

105

-5

5

5

116

106

10

10

4

100

105

-5

5

5

103

106

-3

3

5

100

106

-6

6

4

107

105

2

2

5

103

106

-3

3

5

100

106

-6

6

4

88

105

-17

17

5

100

106

-6

6

4

100

105

-5

5

4

109

105

4

4

5

103

106

-3

3

4

97

105

-8

8

4

103

105

-2

2

4

108

105

3

3

4

103

105

-2

2

3

100

104

-4

4

5

100

106

-6

6

4

102

105

-3

3

4

106

105

1

1

5

120

106

14

14

3

112

104

8

8

6

100

107

-7

7

Total=310

Right-handed

Left-handed

PMCC

0.1104

0.0350

Difference between line of best fit and the other co-ordinates

642

310

Both also have a low positive correlation, but the right-handed have a
higher correlation. Although there the right-handed have a higher
correlation than the left-handed, but the left-handed have a higher
difference in the co-ordinates.

Final Conclusion for aim 2

After working out the PMCC, scatter diagram and find out the
difference between the co-ordinates and the line of best fit. We found
out there's no correlation between the IQ and English Key Stage
result; IQ and Maths Key Stage result and IQ and the Science Key Stage
result. Even though they have a positive correlation, but it's a low
correlation, so it can't proves anything that is important.

Aim 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

What I will do is collect 60 people who like red, and calculate the
percentage of left-handed who like red and calculate the % of
right-handed who like red.

After choosing the data randomly, we got 60 people who like red.

11 of them are left-handed

49 of them are right-handed

The percentage of left-handed in the overall people who like red is

11/60 x 100%=18%

The percentage of right-handed in the overall people who like red is

49/60 x 100% = 82%

After calculating these results, we can see that the % of left-handed
who like red is only 18%, which is even less than a 50%, so not more
left-handed people like red than the right-handed.

In order to give a more obvious answer, I will plot a Pie chart to
show my answer more clearly.

Conclusion, the statement is incorrect because in this investigation,
more right-handed like red more than left-handed.

Aim 4)The subjects " Design & Technology", "Art" and "Music" always
require

creativity. More left-handed people like these subjects.

First find 20 people who study Design & Technology

20 people who study Art

20 people who study music

Then calculate the percentage of left-handed and right-handed.

Design of Technology:20 people: 12 left-handed =60%

8 right-handed=40%

Art: 20 people: 15 left-handed=75%

5 right-handed=25%

Music: 11 left-handed=55%

9 right-handed=45%

Then we will plot graphs to show the % of left-handed and right-handed

From the data, we can see more left-handed like these creative
subjects than right-handed.

In follow up statement, I can say because these are the subjects which
require creativity, and more left-handed people like these subjects,
so they may be more creative.

Final Conclusion

My diagrams and calculations have helped me to show that:

Aim 1:

From the Box and Whisker diagram and calculating the IQR, I can
conclude that the range of the IQ of the right-handed is spread wider
than the left-handed, since it has a higher IQR. In the Box and
Whisker diagram, both of them have a positive skew, that means the
data the left-handed and the right-handed are having, are higher than
the median. Also from the box and whisker diagram, it shows that more
than 75% of the IQ of the left-handed is higher than the IQ of the
right-handed median.

From comparing the histograms of the left-handed and right-handed, I
can say most of the IQ of both left-handed and right-handed are
concentrated between the range 100-120 and the data of the left-handed
is even more concentrated than the right-handed between the range
100-110.

In the calculation of standard deviation and mean, I found out the
mean of the left-handed is higher than the right-handed, it shows the
average of the left-handed is higher. Overall it reflects the IQ of
the left-handed is higher than the right-handed practically.

The reason that I didn't compare the range of the standard deviation
since it may contains some small extreme data, so the result was the
left-handed data is more spread out than the right-handed.

Aim 2:

The Scatter Diagram helped us to show the correlation between the KS2
results and the IQ and it shows how the data distributed.

By calculating the PMCC, we can know the correlation, if it is high,
low, positive or negative correlation.

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.

How to Cite this Page

MLA Citation:
"Comparing Left-Handed and Right-Handed People." 123HelpMe.com. 26 Nov 2014
    <http://www.123HelpMe.com/view.asp?id=122342>.




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