There are 200 pupils in Year 10: 96 are girls and 104 are boys:
Girls = 96/200 x 50
= 24
Therefore I will use 24 pieces of data from the girls.
Boys = 104/200 x 50
= 26
Therefore I will use 26 pieces of data from the boys.
The minimum value for the girl’s box plot here is 79 and the maximum value is 113. The LQ is 93 and the UQ is 103; the IQR being 10. There is an outlier at either end: the low one being at 69 and the high one being at 120. The mean is 98.72 and the SD is 10.8. For the boy’s box plot, the lowest value is 78, the highest value being 117. The LQ is 90 and the 104; the IQR being 14 and the median being100. The mean is 98, the SD is 10.01 and there are no outliers.
The IQ’s of Year 10 girls and boys are very similar. The median are exactly the same and there is little variation with the length of the whiskers – suggesting that neither gender is more intelligent than the other. Nevertheless, the girls have outliers (including a very low one) which leads to the conclusion that they are more intelligent in Year 10.
There are 172 pupils in Year 11: 85 are girls and 87 are boys:
Girls = 85/172 x 50
= 25
Therefore I will use 25 pieces of data from the girls.
Boys = 104/200 x 50
= 25
Therefore I will use 25 pieces of data from the boys.
The lowest value for the girls in this box plot is 82, the highest is 109 and the median is 100.5. The LQ is 96.25 and the UQ is 105.5, therefore the IQR is 9.25. There is also a low outlier at 81, a mean of 99.2 and a SD of 7.7. The boy’s minimum value is 84, the highest value is 118 and the median is 101. The LQ is 100 and the UQ is 107.5; the IQR being 7.5. The mean is 102, the SD is 8.9 and there are no outliers.
When comparing these two box plots, I found that the medians are close together. However the highest value and lowest value are higher for boys than for girls (whilst girls have the higher IQR). Also the girls in Year 11 have a low outlier, point to the fact that the boys are more intelligent in Year 11 than girls.
In conclusion, there is not a single gender that is the most intelligent overall: each year is different. My data suggests that Females are more intelligent in Years 7-10 but Males are more intelligent in Year 11. However this may not be the case, as I had to sample my data in order to make it easy to work with; the rest of the data may show the opposite case. My sample was unlikely to be large enough to represent the population fairly and if someone else were to do this hypothesis, it is likely that they would get different results. If I were to re-do this hypothesis, I would not have taken a sample, as this can alter the results.
- To see whether my second hypothesis is true, I will plot the IQ against the KS2 Results on a scatter graph. As there are 3 possible values for the KS2 results (all of which are discrete data), I will simply use the KS2 Mathematics data. The data will be grouped according to Year and gender I will plot and analyze the graphs on Microsoft Excel. I will use the PMCC to see whether there is a good relationship between the two sets of data. If the PMCC returns a value of 1, it is a strong positive correlation. A value -1 will show that the graph has a strong negative correlation and a value of 0 shows it has no correlation. As it is easy to create on the computer. I am doing each year separately, so I will therefore not be sampling data for this hypothesis. I will work out the SD and PMCC for each graph, using Microsoft Excel. I hope that my graphs will show a correlation between IQ and KS2 results, whether it is a positive or negative correlation.
The first scatter graph shows the Year 7 Male IQs against their respective KS2 Maths result. The KS2 Maths results ranges from 2 to 5 and the IQs range from 68 to 117. The lowest KS2 Maths result is also the lowest IQ result; the same being with the highest result. The PMCC is 0.747 this shows that there is a strong relationship between the variables in a positive direction: this is shown with the line of best of fit. The results are most densely distributed around the linear where it crosses through the integers on the x axis. There are a few results which are quite far away from the line of best fit. The results are most densely distributed at 3 on the x axis and 95 on the y axis. The SD for the Male IQ is 7.928 and for the KS2, the SD is 0.739 which shows that the results are closely distributed.
The second scatter graph shows the results for the Year 8 Female IQs against their respective KS2 Maths results. There is a larger range on this scatter diagram than on the one showing the Male results: the girls have a higher range for their IQs and similarly for their KS2 Maths results. The lowest value on the y axis is also the lowest result on the x axis but the highest value on the x axis is not the highest on the y axis. The PMCC for this graph is 0.719 which tells us that there is a relationship between the two variables in a positive direction. It also tells us that as the IQs get larger so do the KS2 Maths results. From the PMCC linear we can see that there are some results which are far away, but the large majority are placed on or around the linear. The results are most densely distributed around the 4 and 5 on the x axis and the 100 to 110 on the y axis. The SD for the Female IQ is 8.25 and the SD for their KS2 is 0.739, showing that the results are quite densely distributed.
When we compare these two scatter diagrams we can see that the Female results have a larger range of IQ than the Males but they both have the same range for their KS2 Maths results. Both the graphs are most densely distributed around the median of the array of data. There are a few results which are quite far away from the line of best fit, but there could be a number of reasons why this is. It could be that they did poorly on an exam which suggests high IQ and low KS2 Result. On the other hand, a high KS2 result and low IQ could suggest a lot of revision for an exam The PMCC for the Males is larger than the PMCC for the Females which shows that there is a stronger relationship between the Male IQs and KS2 Maths results than between the Female IQs and KS2 Maths results. This is shown on the graph by the PMCC linear being more positively drawn on the Male graph than the Female graph. The SD for the Male IQ is lower than the SD for the Female IQ and is the same for their KS2 results. This shows that the Male IQ are more evenly and closely distributed than the Female IQ and their KS2 results have a similar variation. In Conclusion, this shows us that the relationship between the IQ’s and KS2 Results are more closely related for Males than for Females.
The first scatter graph shows the Year 8 Male IQs against their respective KS2 Maths result. The KS2 Maths results ranges from 2 to 6 and the IQs range from 71 to 113. The lowest KS2 Maths result is also the lowest IQ result; however the highest IQ is not the highest KS2 result. The PMCC is 0.764 this shows that there is a strong relationship between the variables in a positive direction: this is shown with the line of best of fit. The results are most densely distributed around the linear where it crosses through the integers on the x axis. However, there are a number of results which are quite far away from the line of best fit. The results are most densely distributed at 3 on the x axis and 100 on the y axis. The SD for the Male IQ is 9.023 and their KS2 results are 0.708; which shows that the results are closely distributed.
The second scatter graph shows the results for Female IQs against their KS2 Maths results. There is a smaller range on this scatter diagram than on the one showing the Male results and the data is less clustered around the line of the best fit. The girls have a higher range for their IQs but a smaller range for their KS2 Maths results. The lowest value on the y axis is also the lowest result on the x axis and the highest value on the x axis is also the highest on the y axis. The PMCC for this graph is 0.722 which tells us that there is a relationship between the two variables in a positive direction. It also tells us that as the IQs get larger, so do the KS2 Maths results. From the PMCC linear, we can see that there are many results which are far away; a small majority are placed on or around the linear. The results are most densely distributed around the 3,4 and 5 on the x axis and the 100 to 115 on the y axis. The SD for the Female IQ is 9.023 and their KS2 is 0.708, showing that the results are quite densely distributed.
When we compare these two scatter diagrams we can see that the Female results have a larger range of IQ than the Males but the Males have the higher range for their KS2 Maths results. Both the graphs are most densely distributed around the median of the array of data. There are a few results which are quite far away from the line of best fit, but there could be a number of reasons why this is. It could be that they did poorly on an exam which suggests high IQ and low KS2 Result. On the other hand, a high KS2 result and low IQ could suggest a lot of revision for an exam. The PMCC for the Males is larger than the PMCC for the Females which shows that there is a stronger relationship between the Male IQs and KS2 Maths results than between the Female IQs and KS2 Maths results. This is shown on the graph by the PMCC linear being more positively drawn on the Male graph than the Female graph. The SD for the Male IQ is higher than the SD for the Female IQ and for the KS2 results. This shows that the Female results are more evenly and closely distributed than the Male results. In Conclusion, this shows us that the relationship between the IQ’s and KS2 Results are more closely related for Males than for Females.
The first scatter graph shows the Male IQs against their respective KS2 Maths result. The KS2 Maths results range from 2 to 6 and the IQs range from 68 to 126. The lowest KS2 Maths result is also the lowest IQ result but the highest KS2 Maths result is not the highest IQ result. The PMCC is 0.779, showing that there is a strong relationship between the variables in a positive direction: this is also shown with the line of best of fit. The results are most densely distributed around the linear where it crosses through the integers on the x axis. There are a few results which are quite far away from the line of best fit. The results are most densely distributed at 4 on the x axis and 97 on the y axis. The SD for the Male IQ is 9.678 and 0.806 for their KS2 results which shows that the results are closely distributed.
The second scatter graph shows the results for Female IQs against their KS2 Maths results. There is a smaller range on this scatter diagram than on the one showing the Male results: the girls have a higher range for their IQs and the same range for their KS2 Maths results. The lowest value on the y axis is also the lowest result on the x axis and the highest value on the x axis is also the highest on the y axis. The PMCC for this graph is 0.837 which tells us that there is a relationship between the two variables in a positive direction. It also tells us that as the IQs get larger so do the KS2 Maths results. From the PMCC linear we can see that there are some results which are far away, but the large majority are placed on or around the linear. The results are most densely distributed around the 4 and 5 on the x axis and the 100 to 110 on the y axis. The SD for the Female results is 10.175 for the IQ and 0.774 for the KS2 results: showing that the results are quite densely distributed.
When we compare these two scatter diagrams we can see that the Female results have a smaller but higher range of IQ than the Males but both have the same range for their KS2 Maths results. Both the graphs are most densely distributed around the median of the array of data. There are a few results which are quite far away from the line of best fit, but there could be a number of reasons why this is. It could be that they did poorly on an exam which suggests high IQ and low KS2 Result. On the other hand, a high KS2 result and low IQ could suggest a lot of revision for an exam. The PMCC for the Females is larger than the PMCC for the Males which shows that there is a stronger relationship between the Female IQs and KS2 Maths results than between the Male IQs and KS2 Maths results. This is shown on the graph by the PMCC linear being more positively drawn on the Female graph than the Male graph. The SD for the Male IQ is lower than the SD for the Female IQ but higher for the KS2 results. This shows that the Female KS2 results are more evenly and closely distributed than the Male results but the Male IQ’s are more evenly distributed.. In Conclusion, this shows us that the relationship between the IQ’s and KS2 Results are more closely related for Males than for Females.
The first scatter graph shows the Male IQs against their respective KS2 Maths result. The KS2 Maths results range from 2 to 6 and the IQs range from 74 to 131. The lowest KS2 Maths result is the lowest IQ result and the highest KS2 Maths result is also the highest IQ result. The PMCC is 0.833, showing that there is a strong relationship between the variables in a positive direction: this is also shown with the line of best of fit. The results are most densely distributed around the linear where it crosses through the integers on the x axis. There are a number of results which are quite far away from the line of best fit. The results are most densely distributed at 3 on the x axis and 98 on the y axis. The SD for the Male IQ is 10.298 and the SD for Male KS2 is 0.872 which shows that the results are closely distributed.
The second scatter graph shows the results for Female IQs against their KS2 Maths results. There is a smaller range on this scatter diagram than on the one showing the Male results and the girls have a smaller range for their IQs and for their KS2 Maths results. The lowest value on the y axis is the lowest result on the x axis and the highest value on the x axis is also the highest on the y axis. The PMCC for this graph is 0.88 which tells us that there is a relationship between the two variables in a positive direction. It also tells us that as the IQs get larger so do the KS2 Maths results. From the PMCC linear, we can see that there are some results which are far away, but the large majority are placed on or around the linear. The results are most densely distributed around 4 on the x axis and the 100 on the y axis. The SD for the Female IQ is 8.632 and the KS2 results is 0.751 showing that the results are quite densely distributed.
When we compare these two scatter diagrams we can see that the Female results have a smaller lower range of IQ than the Males but both have the same range for their KS2 Maths results; both the graphs are most densely distributed around the median of the array of data. There are a few results which are quite far away from the line of best fit, but there could be a number of reasons why this is. It could be that they did poorly on an exam which suggests high IQ and low KS2 Result. On the other hand, a high KS2 result and low IQ could suggest a lot of revision for an exam. The PMCC for the Females is larger than the PMCC for the Males which shows that there is a stronger relationship between the Female IQs and KS2 Maths results than between the Male IQs and KS2 Maths results. This is shown on the graph by the PMCC linear being more positively drawn on the Female graph than the Male graph. The SD for the Males IQ and KS2 results are lower than the SD for the Female IQ and KS2 results, which shows that the Female results are more evenly and closely distributed than the Male results. In Conclusion, this shows us that the relationship between the IQ’s and KS2 Results are more closely related for Males than for Females.
The first scatter graph shows the Male IQs against their respective KS2 Maths result. The KS2 Maths results ranges from 2 to 6 and the IQs range from 75 to 140. The lowest KS2 Maths result is also the lowest IQ result; the highest KS2 mark is, however, not the highest IQ result. The PMCC is 0.789, showing that there is a strong relationship between the variables in a positive direction: this is also shown by the line of best of fit. The results are most densely distributed around the linear where it crosses through the integers on the x axis. There are a few results which are quite far away from the line of best fit. The results are most densely distributed at 4 on the x axis and 105 on the y axis. The SD for the Male IQ is 11.271 and 0.881 for Male KS2 results; which shows that the results are closely distributed.
The second scatter graph shows the results for Female IQs against their KS2 Maths results. There is a much smaller range on this scatter diagram than on the one showing the Male results: the girls have a smaller range for their IQs but a similar size one for their KS2 Maths results. The lowest value on the y axis is the lowest result on the x axis and the highest value on the x axis is also the highest on the y axis. The PMCC for this graph is 0.756 which tells us that there is a relationship between the two variables in a positive direction. It also tells us that as the IQs get larger so do the KS2 Maths results. From the PMCC linear we can see that there are some results which are far away, but not many as the large majority are placed on or around the linear. The results are most densely distributed around the 3 and 4 on the x axis and the 100 on the y axis. The SD for the Female IQ is 7.691 and the SD for Female KS2 results is 0.804, showing that the results are quite densely distributed.
When we compare these two scatter diagrams we can see that the Male results have a larger range of IQ than the Females but they both have the same range for their KS2 Maths results. Both the graphs are most densely distributed around the median of the array of data. There are a few results which are quite far away (especially on the Male graph) from the line of best fit, but there could be a number of reasons why this is. It could be that they did poorly on an exam which suggests high IQ and low KS2 Result. On the other hand, a high KS2 result and low IQ could suggest a lot of revision for an exam. The PMCC for the Males is larger than the PMCC for the Females which shows that there is more of a relationship between the Male IQs and KS2 Maths results than between the Female IQs and KS2 Maths results. This is shown on the graph by the PMCC linear being more positively drawn on the Male graph than the Female graph. The SD for the Males is higher than the SD for the Females which shows that the Male results are less evenly and more sparsely distributed than the Female results. In Conclusion, this shows us that the relationship between the IQ’s and KS2 Results are more closely related for Females than for Male.
The above diagram shows the line of best fit for both genders of all years. As you can see, each year varies and two are the same. The Year 7 boys have the least correlation between their IQ and KS2 results and the Year 9 Girls have the most correlation. A perfect positive correlation will have the formula “x=y”, whereby for every integer that x increase, y increases by the same; the orange line (representing the Year 9 Girls) is most like this. If you compare the PMCC, you will find that the Year 9 Girls will have the value closest to 1. In conclusion, there is more of a correlation between the KS2 Maths results and IQ for Males than Females. This means that the majority of girls are likely to have increased their IQ’s since KS2, meaning that they learn quickly and better compared to boys.
- To see whether my third hypothesis is true, I will plot the IQ against the Hours of TV watched on a scatter graph. I will take a sample because I am plotting 2 graphs (one for Males and Females) for all years and to put over 500 points on a scatter graph will clutter it and make it illegible; my sample size will be 50 for each gender. However, this may not necessarily be a true representation of the data. I will use the PMCC to see whether there is a good relationship between the two sets of data. If the PMCC returns a value of 1, it is a strong positive correlation. A value -1 will show that the graph has a strong negative correlation and a value of 0 shows it has no correlation. As it is easy to create on the computer; I will also work out the SD. I will be using Microsoft Excel to create the graphs and work out any calculations. I hope that my graphs will show a correlation between IQ and hours of TV watched, whether it is a positive or negative correlation.
- There are 604 boys in Mayfield High.
Year 7: = 151/604 x 50
= 13
Year 8: = 145/604 x 50
= 12
Year 9: = 118/604 x 50
= 9
Year 10: = 106/604 x 50
= 9
Year 11: = 84/604 x 50
= 7
The data above will be used to calculate my samples from each gender from each year.
The first scatter graph shows the Male IQs against how many hours of TV they watch per week. The TV results range from 0 to 48 and the IQs range from 68 to 126. The lowest and highest are not the lowest IQ result respectively. The PMCC is 0.0504, showing that there is a very weak negative correlation between the two sets of data. The results are most densely distributed at 100 on the x axis and 13 on the y axis. The SD for the Male IQ is 10.511 and 10.544 for their KS2 results which shows that the results are sparsely distributed.
The second scatter graph shows the results for Female IQs against their hours of TV viewed. There is a smaller range on this scatter diagram than on the one showing the Male results: the girls have a lower range for their IQs and for their hours of TV viewed. Again, neither the highest or lowest value on the x axis is the highest or lowest on the y axis. The PMCC for this graph is 0 which tells us that there is no correlation between the two sets of data. The results are most densely distributed around the 100 on the x axis and the 21 on the y axis. The SD for the Female results is 8.9 for the IQ and 10 for the hours of TV viewed: showing that the results are quite randomly distributed.
When we compare these two scatter diagrams we can see that the Female results have a smaller for their IQ’s and hours of TV watched than Males There are a few results which are quite far away from majority, but there could be a number of reasons why this is. It could be that they did poorly on an exam which suggests a low IQ. On the other hand, a high IQ could suggest a lot of revision for an exam. Watching TV may not always be a bad thing. One person may watch 7 hours of cartoons or soaps each week whilst another may watch 40 hours of educational programs. The PMCC for the Males is slightly smaller than the PMCC for the Females which show that there is a stronger negative relationship between the Male IQs and hours of TV than between the Female IQs and hours of TV. However, the male result is very low and the female result is 0, so the males only just have a negative correlation. The SD for the Male IQ is higher than the SD for the Female IQ and for the hours of TV watched. This shows that the Female results are more evenly and closely distributed than the Male results. In Conclusion, I think that, even though there is a small correlation for boys, that there is no correlation between the Hours of TV watched and IQ; this does not support my original conclusion. Your IQ depends on many things and may or may not be affected by what TV you watch. If it does, it will depend on what type of program you watch, for how long and how well you store the information that is portrayed by the program.
- To see whether my fourth hypothesis is true, I will plot the samples of data on a histogram. I will take a sample of 100 from across the years for both genders (50 from each gender) and use Microsoft Excel to draw the histograms. The data will be grouped by Year Groups and I will draw two histograms – one for Males and one for Females. I will see if the data follows the normal distribution and will also work out the mean and SD for the histograms so I can compare the graphs for the shape of the distribution. I hope that my graphs will show that a specific gender is taller. If it does not show this overall, I hope that I can find a gender that is taller for each year.
- There are 604 boys in Mayfield High.
Year 7: = 151/604 x 50
= 13
Year 8: = 145/604 x 50
= 12
Year 9: = 118/604 x 50
= 9
Year 10: = 106/604 x 50
= 9
Year 11: = 84/604 x 50
= 7
After taking my sample of 50 boys’ heights, I had to calculate the frequency, frequency density, mean and class width to create a histogram. These values are given below:
Table of Values of Histogram for Boys:
Class Int. Mid. Point. (x) Class Width Freq. Freq. Density
1.35 ≤ x < 1.45 1.4 0.1 4 40
1.45 ≤ x < 1.55 1.5 0.1 5 50
1.55 ≤ x < 1.65 1.6 0.1 18 180
1.65 ≤ x < 1.75 1.7 0.1 12 120
1.75 ≤ x < 1.85 1.8 0.1 11 110
I then took a sample of 50 girls’ heights and calculated the same values which are shown below:
Table of Values of Histogram for Girls:
Class Int. Mid. Point. (x) Class Width Freq. Freq. Density
1.35 ≤ x < 1.45 1.4 0.1 1 10
1.45 ≤ x < 1.55 1.5 0.1 9 90
1.55 ≤ x < 1.65 1.6 0.1 30 300
1.65 ≤ x < 1.75 1.7 0.1 9 90
1.75 ≤ x < 1.85 1.8 0.1 1 10
The lower classes on the boys’ histogram have a fairly low FD compared to the higher classes. The modal class is 1.55 ≤ x < 1.65. The SD is 0.1168 and the mean is 1.642, which shows that the results are a bit skewed but fairly centred on the mean.
The female histogram has a normal distribution with a mean of 1.6 an SD of 0.0721, which shows that the results are very closely distributed around the mean. The modal class is, again, 1.55 ≤ x < 1.65, showing that the majority of the pupils have an average height. The classes 1.45 ≤ x < 1.55 and 1.55 ≤ x < 1.65 are higher for girls than boys but the other three classes are lower: because the female histogram follows the normal distribution. Therefore, I believe that girls are taller than boys in general.
In Conclusion, I have been able to fully support 3 of my 4 hypothesis; my third hypothesis has been disproved. Throughout my coursework I have used a range of calculations and graphs in the appropriate places which are useful and have supported my hypotheses to their full extent. I have hand drawn my Box and Whisker Plots because I have to hand draw some of them but also because it is much easier to do them by hand. There are some limits to my work because I had to sample some of my data. This was done for various reasons a few times, mainly to make my work easier to understand. The problem with sampling is that it does not give a full and fair representation of the population though the results may be the same as the un-sampled data; it is likely that is not as you do not use the entirety of the data available. Improvements could have been made to my hypotheses. I think that I have used all the best methods possible and used them to the best of my abilities.
