Girl’s total key stage 2 results are better if their IQ is higher
For this extension to my first hypothesis I will see if girl’s key stage 2 results are better if they have a high IQ, as my first graph included boy’s and girl’s I would like to see if the same trend carries on for girl’s or if there is any difference.
I separated all of the males from the females and once again I took a random sample of 50 girls using Microsoft Excel. The girl’s key stage 2 results were added up using the auto sum button.
Graph 2: Scatter diagram to show correlation between girls’s IQ and their total key stage 2 results.
From graph 2 we can see that there is a correlation between girls’s IQ and their total key stage 2 results. The graph suggests that if girls have a high IQ their total key stage 2 results will be higher.
Boys’ total key stage 2 results are better if their IQ is higher
For the third part of my hypothesis I will see if the same trend, which is if students IQ is higher their key stage 2 results are higher, will carry on for boy’s. To obtain my random sample of 50 boys I will be following the same steps as for my previous samples, separating the genders and then choosing 50 random boys in excel and totalling their key stage 2 results.
Graph 3: Scatter diagram to show correlation between boys’s IQ and their total key stage 2 results.
From graph 3 we can see that there is a correlation between boys’s IQ and their key stage 2 results. The graph suggests that if boy’s have a high IQ their keys stage 2 results will be better.
Students' key stage 2 math results are better if their IQ is higher
For this hypothesis I have decided to, firstly take a random sample of 50 students to see the correlation between their IQ and their key stage 2 maths results. The reason for picking maths rather than Science or English is that many of the questions in the IQ test are quite math orientated. Due to this people who are good at maths should get a high IQ and a good key stage 2 maths result.
Graph 4: Scatter diagram to show correlation between students IQ and their key stage 2 math results.
Graph 4 shows that there is positive correlation between IQ and students key stage 2 math results. We can clearly see that the higher the IQ the higher their key stage 2 math result.
The sample used in graph 4 was of both boys and girls, now I will take random samples of both 50 boys and girls to see if the trend continues for both genders separately.
Graph 5: Scatter diagram to show correlation between girls IQ and their key stage 3 math results.
Graph 5 shows that girls that have a high IQ generally have good key stage 2 math results. Although some of the points seem far away from other points these outliners are not anomalous results because just because these outliners are far away form other points they are still close to the line of best fit. To avoid having these outliners I could have extended my sample so that maybe it would fit the general trend better.
Graph 6: Scatter diagram to show correlation between boys IQ and their key stage 2 math results.
Graph 6 shows that boys who have a high IQ will generally have a high key stage 2 math result. Again there are a few outliners but they are close to the line of best fit although they are far away from other points. Yet again if I extended my sample the general trend might show more clearly.
The boys and girls samples are quite equally matched so it’s hard to tell if out of graphs 5 and 6 which of the two genders performs better.
A better way of comparing the boys and girls is by using a histogram. I will be creating two histograms; one of girls IQ and the other of boys IQ, this will hopefully show us which gender has the best overall IQ.
Boys generally have higher IQs than girls
For this hypothesis I have decided to make two separate histograms in frequency, not in frequency density, I will do this for both genders. The reason being that IQ is continuous and its easier to group it together in intervals, these are my results:
Graph 7: Histogram of boy’s IQ.
It’s quite clear that there has been some anomalous data in graph 7; we can see this by the rise in frequency at the beginning of the graph.
Due to this I was not able of edit the x axis of the graph making it clearer to see and easier to read.
Graph 8: Histogram of girl’s IQ.
Graph 9: Frequency polygon for girl’s and boy’s IQ.
Looking at the two histograms and at the polygon it suggests that girls IQ are generally higher than boys IQ. In the histograms I used a sample of 100 boys and 100 girls, and in the polygon these samples were put into one graph. Since the sample was totally random, a poor performing 100 boys may have been selected and also a high performing 100 girls may have been selected.
Although the samples were totally fair, as they were both random, and the graphs show that girls IQ are generally higher than boys IQ an even larger sample would have been more useful and would have been more representative of both genders, also stratified sampling could have been used.
Boys will generally have higher total key stage 2 results than girls
I decided that a cumulative frequency graph would be ideal for this hypothesis as it’s a really good way of comparing two different sets of results.
Graph 10: Cumulative frequency of total key stage 2 results for boys and girls.
As the quartiles are easily read off cumulative frequency graphs I will do a box and whisker diagram.
Graph 11: Box and whisker diagram for total key stage 2 results for boys and girls.
The results suggest that the gender which has the highest total key stage 2 results is the girls. The cumulative frequency curves show that the boys curve rose more steeply form the 6-12 total key stage 2 result region. The girls curve began to rise quickly at the 12-16 key stage 2 result region, in this same region the boys curve was rising slightly slower, this suggests that the boys didn’t have as many people in this region.
The girls have a higher mean than the boys, the reason being because their key stage 2 results are not as spread out, they are rather bunched together. If you look at the boy’s box and whisker diagram there is a substantial difference in the size of their box, it’s a long way bigger than the girls. The reason for this is because the inter-quartile range for the girls was 1.92 while the boy’s inter-quartile range is 3.27.
All of the graphs suggest that girls have higher key stage 2 results than boys, therefore, my hypothesis was wrong.
Conclusion
Students' total key stage 2 results are better if their IQ is higher. – Girl’s total key stage 2 results are better if their IQ is higher. –Boy’s total key stage 2 results are better if their IQ is higher.
