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. 24 May 2013 <http://www.123HelpMe.com/view.asp?id=122342>. |
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