Comparing LeftHanded and RightHanded People
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Are lefthanded people more intelligent and creative than the righthanded 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 lefthanded people have a higher IQ than the righthanded? 2) There is a correlation between the IQ and the Key Stage 2 results for the lefthanded 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 lefthanded people like "red" than righthanded. 4) The subjects " Design & Technology", "Art" and "Music" always require creativity. More lefthanded 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 righthanded in Year 7, 8 and 9 Number of Boys Number of Girls Total % of certain year of boys in the total of the righthanded % of certain year of girls in the total of the righthanded 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 How to Cite this Page
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lefthanded and 8% of the righthanded. Having the same amount of data
can have fair results. For the righthanded, 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 righthanded. Stratifying the lefthanded people in year 7,8 and 9 Number of Boys Number of girls Total % of certain year of boys in the total of the lefthanded % of certain year of girls in the total of the lefthanded 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 lefthanded 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 lefthanded data I will have to collect to collect the following information Aim 1: 60 IQ of the lefthanded and 60 IQ of the righthanded in Year 7,8 and 9. Aim 2: 60 people of the IQ of the lefthanded and 60 people of the IQ of the righthanded.  Key Stage results [English] [Maths] [Science] of the lefthanded and the righthanded 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 lefthanded and 60 people of the IQ of the righthanded. Aim 2: 60 people of the IQ of the lefthanded and 60 people of the IQ of the righthanded. Key Stage results [English] [Maths] [Science] of the lefthanded and the righthanded 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 lefthanded and the righthanded. I will use this data to compare  Aim 1: Comparing the mean of the IQ of the lefthanded people and the IQ of the righthanded people. As if the IQ of the lefthanded 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 lefthanded and the righthanded. Aim 3: Calculating the percentages of lefthanded and righthanded who likes red and find out the answer. Aim 4: Comparing in the "Creative Subjects", do more lefthanded people take these subjects than the righthanded? By calculating the percentage of lefthanded and righthanded 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 lefthanded and the median of the IQ of the righthanded Calculate the Upper Quartile and the Lower Quartile of the Data. Calculate the IQR of both lefthanded and righthanded Compare the IQR of the IQ of the lefthanded and the righthanded, to see how their data is spread and to see how much the data is concentrated about the median. Do another table for lefthanded. 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 lefthanded and the righthanded, 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 lefthanded and righthanded. Find the percentage of the lefthanded and righthanded 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 lefthanded and righthanded. Work out the percentage of how many of them is lefthanded or righthanded. 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 lefthanded is cleverer than the righthanded 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 lefthanded and righthanded. 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 lefthanded people and righthanded 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 lefthanded and the righthanded Aim 2: Compare the PMCC and correlation of the lefthanded and the righthanded, 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 lefthanded and righthanded into different group and I can calculate the Cumulative Frequency. Righthanded Class Interval of IQ Frequency Cumulative Frequency 010 0 0 1020 0 0 2030 0 0 3040 0 0 4050 0 0 5060 0 0 6070 2 2 7080 1 3 8090 6 9 90100 24 33 100110 23 56 110120 3 59 120130 1 60 Lefthanded Class Interval of IQ Frequency Cumulative Frequency 010 0 0 1020 0 0 2030 0 0 3040 0 0 4050 0 0 5060 0 0 6070 0 0 7080 0 0 8090 2 2 90100 20 22 100110 28 50 110120 10 60 120130 0 60 In the first graph, Cumulative Frequency Curve of the IQ of the Righthanded I found the Lower Quartile the Upper Quartile the Interquartile Range the Median of the righthanded Lower Quartile: In total, there are 60 data. To find the LQ, we must calculate 60 x 25%=15, then cross the yaxis from 15 till it meets the curve. When it meets the curve, vertical down till it meets the xaxis. Read the xintercept, and that's the LQ. Upper Quartile: There are 60 data in total, to find the UQ, calculate 60x75% =45. Cross the yaxis from 45 till it meets the curve. When it meets the curve, vertical down till it meets the xaxis. Read the xintercept 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 Lefthanded I found the Lower Quartile the Upper Quartile the Interquartile Range the Median of the lefthanded 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 lefthanded and righthanded by Box and Whisker diagram From the comparing of the Box and Whisker Diagram of the lefthanded and the righthanded We can comment: Å¸ Both of them have a positive skew, but the lefthanded have a have a higher positive skew than the righthanded. The skew of the righthanded is almost medium, but it is still a positive skew. The skew of the lefthanded is showed clearly, we can classify it as a positive skew easily. Å¸ From the lefthanded and righthanded box and whisker diagram, both of them are positive skew, so they have higher mean than median Å¸ The range and IQR of righthanded IQ is bigger than the lefthanded IQ. That shows the range of the lefthanded IQ is much more concentrated and the data is not spread out widely. Å¸ More than 75% of the lefthanded IQ is higher than the median IQ of the righthanded. 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 lefthanded IQ and the righthanded IQ to calculate the frequency density. Then we can start to draw the two histograms. One for the lefthanded and one for the righthanded. Frequency Density= Frequency / Class interval Lefthanded IQ Class Interval Frequency Frequency Density 080 8 3 0.4 8090 1 6 6 90100 1 24 24 100110 1 28 28 110130 2 10 5 Righthanded IQ Class Interval Frequency Frequency Density 080 8 0 0 8090 1 2 2 90100 1 20 20 100110 1 28 28 110130 2 10 5 After looking into the histograms of the lefthanded and the righthanded I can comment: Å¸ Both of the lefthanded and the righthanded are concentrated in the IQ range 90100 and 100110 Å¸ The data in the lefthanded is more concentrated in 100100 then the right handed , The Overall data for the righthanded is more spread out than the lefthanded. Å¸ The overall distribution after lefthanded is more concentrated than the righthanded. 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 lefthanded and the righthanded. See whether which is more spread out and compare the mean of the IQ of the lefthanded and righthanded. Find out if the righthanded or lefthanded has a higher average. Formula to calculate the Mean Formula for Mean: âˆ‘ xn n Formula for Standard Deviation: âˆ‘ 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 righthanded Mean: âˆ‘ 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) âˆ‘ xn n = 5949 60 =99.15 The mean of the righthanded is 99.15 Standard deviation of the IQ of the righthanded  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 âˆ‘x2 = the sum of all the square of above data = 595483 then in âˆ‘x2 n n= number of values =60 âˆ´ âˆ‘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 righthanded _____________________ âˆš9924.716667  9830.7225 _________ =âˆš93.99416666 =9.6595058879 After calculating the Standard Deviation of the IQ of the righthanded I will calculate the Mean and Standard Deviation of the IQ of the righthanded IQ of the lefthanded: 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 âˆ‘ xn n = 6249 60 =104.15 Then calculate the Standard Deviation The xvalues 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 âˆ‘x2 in the formula âˆ‘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 âˆ‘x2 n 663727 = 60 =11062.1167 _ (x)2 =10847.2225 _ âˆ‘x2  (x)2 n = 11062.116710862.1167 =200 Square Root 200 to find the standard deviation âˆš200 =14.14213562 The standard deviation for IQ of the lefthanded IQ of Lefthanded IQ of Righthanded 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 Lefthanded is obviously than the righthanded. The higher the standard deviation, that means the higher the data is spread. These results show the data of the lefthanded spread wider than the righthanded since the S.D. of the lefthanded is higher than the righthanded. Then we compare the mean of the lefthanded and the righthanded. The lefthanded have a higher mean than the righthanded. I can conclude that the overall average of the IQ of the lefthanded is higher than the righthanded. The IQ of the lefthanded is 104.15 and the IQ of the righthanded is 99.15. The lefthanded in average, have about 5 IQ higher than the righthanded. Only 60 data is collected, so I can say, the IQ that the lefthanded are higher than the righthanded is 60 x 5=300 in the overall data, and in comparing the lefthanded and the righthanded IQ individually, form the data, I can say each lefthand has 5 IQ higher than the righthanded, 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 Lefthanded Righthanded S.D. 14.14213562 9.659505887 IQR 8 13 The IQR of the IQ righthanded is 62.5% higher than the IQ of the lefthanded. That means the data is more spread out in the righthanded But the S.D. of the IQ of the lefthanded is 46% higher than the righthanded. It shows the data in the lefthanded 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 righthanded 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 righthanded is spread wider than the lefthanded, since it has a higher IQR. In the Box and Whisker diagram, both of them have a positive skew, that means the data the lefthanded and the righthanded 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 lefthanded is higher than the IQ of the righthanded median. From comparing the histograms of the lefthanded and righthanded, I can say most of the IQ of both lefthanded and righthanded are concentrated between the range 100120 and the data of the lefthanded is even more concentrated than the righthanded between the range 100110. In the calculation of standard deviation and mean, I found out the mean of the lefthanded is higher than the righthanded, it shows the average of the lefthanded is higher. Overall it reflects the IQ of the lefthanded is higher than the righthanded 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 lefthanded data is more spread out than the righthanded. Aim 2: Is there a correlation between the IQ and the Key Stage 2 results for the lefthanded and the right handed? In the investigation of this aim, I am going to do 6 calculations 1) Correlation of the righthanded 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 righthanded 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 lefthanded to righthanded 2) Correlation of the Maths Key Stage results to the IQ of lefthanded to righthanded 3) Correlation of the Science Key Stage results to the IQ of lefthanded to righthanded 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 Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• 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 âˆ‘ represents the sum of a set of values 1) Calculate PMCC of the righthanded 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 Î£x=5949 Î£y=246 Î£xÂ²=595483 Î£yÂ²=1056 Î£xy=24383 Substitute them into the formula Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n 5949 x 246 r = 24383  60_____________ âˆš ã€” 595483  ( 5949)Â²ã€•ã€” 1056  ( 248 )Â²ã€• 60 60 1463103. r = 24383 60_____________ âˆš ã€” 595483  35390601ã€•ã€” 1056  61504ã€• 60 60 r= 24383  24385_______ âˆš ã€”5639.65ã€•ã€” 30.93333334ã€• r= 2___ 417.6759191 r= 0.00479 Aftercalculation, the PMCC for the righthanded 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: 10099 83 =0.2 Extend the line of best fit to till it meets the yintercept Then read out the number, we can find the yintercept And the yintercept 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 xcoordinate that is plotted on the graph Real y means the y means the ycoordinate 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 ycoordinate on the line of best fit and x equals to the xcoordinate of the line of best fit. The forth column Real y line y, then see the difference the y coordinate in the line of best fit and ycoordinate that I have plotted on the graph Real x Real y y= 0.2 x + 99 Real y  line y âˆšy2 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 coordinate of the data and the coordinate of the line of best fit is 374.2 Now we investigate the correlation between the lefthanded 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 lefthanded 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 Î£y=253 Î£x=6249 Î£yÂ²=1127 Î£xÂ²=65337 Î£xy=26395 Formula for PMCC Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n Substitute all the numbers into the formula (6249)(253) r = 26395  60 _____________ âˆš ã€” 653327  ( 6249 )Â²ã€•ã€” 1127 ( 253 )Â²ã€• 60 60 r = 26395  26349.95_____________ âˆš ã€” 653327 650833.35ã€•ã€” 11271066.816667ã€• r = 45.05_______________________ âˆšã€”2493.65ã€•ã€” 60.183333ã€• r = 45.05_______________________ 387.3966561 r=0.1163 (cor. to 4 d.p.) The PMCC for the lefthanded 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) 103101 53 =0.67(cor. to 2 d.p.) Extend the line of best fit and read out the yintercept yintercept is 101 we have the yintercept 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 coordinate of the data Real y equals to the y coordinate of the data y=0.67x+101 is the formula of the line of best fit The difference between the coordinates of the data and the coordinate of the line of best fit is equal to Real y line y âˆšy2 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 âˆšy2 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 coordinate of the data and the coordinate of the line of best fit is 287.81 Comparing the PMCC and scatter diagram between the lefthanded and righthanded in the correlation of IQ and Key Stage two results The PMCC for the righthanded is 0.00479 and the PMCC for the lefthanded is 0.1163. Both of them have a low correlation. Obviously, the lefthanded 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 righthanded is more spread out than the lefthanded, we can prove that by calculating the differences between the coordinates on the line of best fit and the coordinates 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 Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n I will find the PMCC of the Maths KS2 result to IQ of the lefthanded and righthanded, then compare them. First I am going to draw a table for righthanded, let x be the Key Stage 2 result and y be the IQ of the righthanded 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 Î£x=251 Î£y=5949 Î£xÂ²=1077 Î£yÂ²=595483 Î£xy=24924 Substitute the collected data into the formula Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n 251(5949) r = 24924  60 _____________ âˆš ã€” 1077  ( 251 )Â²ã€•ã€” 595483  ( 5949 )Â²ã€• 60 60 r = 37.35_____________ âˆš ã€” 26.98333334ã€•ã€”5639.65ã€• 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: 103100 43 =3 Extend the line of best fit till it meets the yintercept Then read out the number, we can find the yintercept And the yintercept 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 coordinate of the points that wasn't on the line of best fit. Real y represents the y coordinate 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 âˆšy2 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 coordinate of the data and the y coordinate of the line of best fit is 548. Next I will calculate the PMCC of lefthanded and then compare it with the righthanded 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 Î£x=248 Î£y=6249 Î£xÂ²=1056 Î£yÂ²=653327 Î£xy=25878 Substitute all these data into the formula Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n 248(6249) r = 25878  60_____________ âˆš ã€”1056  ( 248)Â²ã€•ã€” 653327 ( 6249 )Â²ã€• 60 60 r = 48.8__________________________ âˆš ã€” 30.93333334ã€•[ 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 coordinates from the line of best fit and calculate the slope (3, 101) (4, 103) Slope: 103101 43 =2 After the extension of line of best fit, the yintercept 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 coordinate and the y coordinate on the line of best fit Real x Real y y=2x+99 Real y  line y âˆšy2 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 coordinate of the data and the coordinate of the line of best fit is 341. Comparing: Righthanded Lefthanded PMCC 0.0957 0.1757 Total of Real yline y 548 341 Both of the PMCC of the lefthanded and righthanded have a low positive correlation, but the lefthanded have a higher correlation, that means the data is more concentrated and the data in the righthanded is more spread out than the lefthanded. From the difference of the line of best fit and the total data, we can it clearly that the data of the righthanded is more spread out than the lefthanded. From the graph, the data of the lefthanded is widely spread out than the righthanded. 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 lefthanded and righthanded 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 lefthanded Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• 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 Î£x=259 Î£y=5949 Î£xÂ²=1149 Î£yÂ²=595483 Î£xy=25726 Substitute these data into the formula Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n r = 25726  25679.85_____________ âˆš ã€”1149  ( 259)Â²ã€•ã€”595483  ( 5949 )Â²ã€• 60 60 r = 46.15_____________________________ âˆš ã€”30.98333334ã€•ã€”5639.65ã€• r=46.15 418.0133441 r=0.1104 (cor. to 4 sig. Fig.) Scatter Diagram [IMAGE] Slope: (4.100) (5,103) 103  100 54 slope = 3 yintercept=96 equation for the line of best fit y=3x +96 Real x Real y y=3x+96 Real y  line y âˆšy2 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 lefthanded 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 Î£x=261 Î£y=6249 Î£xÂ²=1161 Î£yÂ²=653327 Î£xy=27192 PMCC Î£x Î£y r = Î£xy  n _____________ âˆš ã€” Î£ xÂ²  ( Î£x )Â²ã€•ã€” Î£yÂ² ( Î£y )Â²ã€• n n r = 27192  27183.15_____________ âˆš ã€”1161  (261 )Â²ã€•ã€” 653327  ( 6249 )Â²ã€• 60 60 r = 8.85____________ ________________ âˆš ã€” 25.65ã€•ã€”2493.65ã€• 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: 102101 54 =1 yintercept=101 Equation y=1(x)+101 Real x Real y y=1x+101 Real y  line y âˆšy2 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 Righthanded Lefthanded PMCC 0.1104 0.0350 Difference between line of best fit and the other coordinates 642 310 Both also have a low positive correlation, but the righthanded have a higher correlation. Although there the righthanded have a higher correlation than the lefthanded, but the lefthanded have a higher difference in the coordinates. Final Conclusion for aim 2 After working out the PMCC, scatter diagram and find out the difference between the coordinates 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 lefthanded people like "red" than righthanded What I will do is collect 60 people who like red, and calculate the percentage of lefthanded who like red and calculate the % of righthanded who like red. After choosing the data randomly, we got 60 people who like red. 11 of them are lefthanded 49 of them are righthanded The percentage of lefthanded in the overall people who like red is 11/60 x 100%=18% The percentage of righthanded in the overall people who like red is 49/60 x 100% = 82% After calculating these results, we can see that the % of lefthanded who like red is only 18%, which is even less than a 50%, so not more lefthanded people like red than the righthanded. 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 righthanded like red more than lefthanded. Aim 4)The subjects " Design & Technology", "Art" and "Music" always require creativity. More lefthanded 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 lefthanded and righthanded. Design of Technology:20 people: 12 lefthanded =60% 8 righthanded=40% Art: 20 people: 15 lefthanded=75% 5 righthanded=25% Music: 11 lefthanded=55% 9 righthanded=45% Then we will plot graphs to show the % of lefthanded and righthanded From the data, we can see more lefthanded like these creative subjects than righthanded. In follow up statement, I can say because these are the subjects which require creativity, and more lefthanded 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 righthanded is spread wider than the lefthanded, since it has a higher IQR. In the Box and Whisker diagram, both of them have a positive skew, that means the data the lefthanded and the righthanded 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 lefthanded is higher than the IQ of the righthanded median. From comparing the histograms of the lefthanded and righthanded, I can say most of the IQ of both lefthanded and righthanded are concentrated between the range 100120 and the data of the lefthanded is even more concentrated than the righthanded between the range 100110. In the calculation of standard deviation and mean, I found out the mean of the lefthanded is higher than the righthanded, it shows the average of the lefthanded is higher. Overall it reflects the IQ of the lefthanded is higher than the righthanded 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 lefthanded data is more spread out than the righthanded. 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 lefthanded and righthanded, we can have a general idea of if more lefthanded people like red or if more righthanded 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 lefthanded have a higher IQ than the median of the righthanded. Overall the average of IQ of the lefthanded is higher. And the range of the lefthanded 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 lefthanded who like red is far away from the righthanded. 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 lefthanded like these subjects than the righthanded. 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. 
