Because there is such a large selection of pupils it would be impossible to compare them all, so I took a random selection of 30 pupils. In truth, it isn't really a fully random decision as I have chosen 15 boys and 15 girls. I didn't use a stratified sample because you obviously cannot have 14.7 pupils, and it was so close to 15. To solve this I took a random selection of 50 boys and 50 girls and picked 15 of each from a hat.
Going from information I have gathered from news and media, I predict that girls on average will attain better results than boys.
Method
Using Microsoft Excel containing data on Mayfield High School I will produce a range of graphs comparing and contrasting different areas of study.
I will display the extracted the extracted information from the Mayfield spreadsheet, and then explain what it shows and what I will do with it. After doing that I will produce a set of graphs to show the correlation between the information, and hopefully I will obtain good correlation and should be able to lead on into further investigations and gain more conclusive information. After this I will conclude my results and explain what I have learnt from them. I will produce mean Key Stage 3 results for every Student.
Fields of Investigation
The fields of investigation will be:
Key stage 3 Results (KS3)
IQ Scores
I hope to find positive correlation with the use of scatter graphs and cumulative frequency diagrams.
Using my random sample of Mayfield High students for both IQ and KS3, I will compile a cumulative frequency Table. I will use this to create a scatter diagram with a line of best fit, this will help me to find the median, lower quartile, upper quartile and inter-quartile ranges. I will be able to compare my data in a different way. Hopefully revealing a difference in correlation between boys and girls.
Cumulative Frequency Tables
I encountered a problem whilst investigating into cumulative frequency charts and that was that Key Stage 3 results are a discrete form of data. To overcome this I made a mean of the 3 results, English, Science and mathematics. This should give my graphs a better verity of results. I could also try a second table and graph of results using totals of KS3 results instead of means, this would make my graphs easier to decipher.
Evaluation
From both my scatter graphs and cumulative frequency curves I can see positive correlation between KS3 results and IQ scores. As a general trend I can say that the higher the KS3 result the higher the IQ. There is always 'outliers' to the trend, for instance a boy with the mean of 3 at KS3 and an IQ of 103. As a trend I can say that boys have a higher IQ and girls have a higher mean of KS3 results. I can see from my scatter graphs that boys IQ's are harder to predict from a KS3 result mean. The box around my scatter graphs show that the girls have a higher correlation because the area of the box is lower meaning the points of the graph are closer.
If I was to increase my sample range of students to 50 or possibly 60 I could achieve a more accurate set of results and graphs to read off median and other ranges. I also achieved better accuracy with my choice of frequency diagrams instead of stem and leaf diagrams.
Using my extended sample of 50 students I can use my findings to make predictions of an IQ for any range of students. I.E. I could find how many boys in the school have an IQ between 100 and 110. My extended results show that 11 boys have an IQ of up to 100 and 27 boys have an IQ up to 110. I used the same method of selecting pupils as used previously.
27 - 11 = 16
(16 ? 38) x 100 = 42.105
Therefor 42.105% of boys in Mayfield high school will have IQs between 100 and 110.
My cumulative frequency graphs prove that the mean IQ of a boy is higher that that of a girl. However, the mean KS3 of a girl is higher than that of a boy.
Conclusion and Further Analysis
My results prove that my original hypothesis was correct, the higher the IQ of a person the better their KS3 would have been. They also tell us that the IQ of a Boy is harder to predict from his KS3 results than it is with a girl. If I had used a mixed sample of Mayfield students I wouldn't have been able to make a prediction of a girl who got a mean of level 4 at KS3's IQ score. For reference her IQ score is predicted to be 99. My scatter graphs prove this with the line of best fit.
I know that a line of best fit has its limitations, but I can use them to predict a mean KS3 result from any boy with a given IQ. I know that the equation of every straight line is y = mx + c . I must use this to find the equations of my lines of best fit. To do this I must look at the point where they intercept the y axis and find the gradients. ( Y = IQ , X = KS3 )
Boys : Y = 10x + 56
Girls : Y = 8x +68
I will now use this equation to find the result for a boy with an IQ of 102. If Y = 102 then….
102 = 10x + 56
Continued….
X = 102 - 56
10
X = 4.6
So a boy with the IQ of 102 should have the mean KS3 result of 4.6, this means that he probably got to 5s and a 4, as 14 ? 3 = 4.6 reoccurring. I can now estimate any IQ from the KS3 mean or vice versa.
Mayfield High School obviously needs to look at the concentration of educational focus between boys and girls, as girls are achieving higher KS3 marks on average. Perhaps if I used a sample of national data I could investigate into the performance of Mayfield High against national means.
