I will use the following tables and graphs to help me in the analysis of my investigation:
They will help me to judge whether levels or IQs are average, above average or below average and this will help with my analysis of medians and modes.
IQ Results
I am going to look at the IQ results individually to determine what the school’s average IQ is. If IQ is related to exam results, it should tell me what kind of results the school has.
The average IQ of everybody is 100. This is a histogram of the IQ’s of my sample. This shows that on average the students at Mayfield School have a higher than average IQ, with some pupils in the category ‘superior’, but having said this, there are still a number of pupils with a ‘low’ IQ. The modal class interval is 100<120.
This box and whisker diagram shows me that the median IQ is 106 which is above average. This suggests that the most students at the school have an above average IQ. The mode which I calculated in Excel is 100.9, which suggests the same as the median, but slightly less over average than the median suggests.
A slightly over average IQ tells me that the school should probably have a slightly over average exam results.
Key Stage 2 Results
By looking at the Key Stage 2 results I should be able to see whether the average IQ is low, average, or high. As I have already found out the average IQ, the graph should show me that the school have a slightly higher than average average exam result.
This is a histogram to show my average Key Stage 2 results of the students in my sample. It shows me that most people scored between a level 4 and a level 5 which is above average as the national average is a level 4.
This box and whisker diagram shows me that the median is 4. This is the national average which suggests that the IQ should be average. The average results range from 3 to 5.3 which tell me that the people in the school have a wide range of ability. The mode which I calculated in Excel is 4.1 which is just over the average.
IQ and Key Stage 2 Results
This scatter diagram shows IQ plotted against average Key Stage 2 result.
There are a few anomalies such as the student with an IQ of 122 (superior) and an average result of 3.7 (under average) and the student with an IQ of 91 (normal-low average) and an average result of 4.7 (over average). This could just be due to the performance of the students on this day.
I am going to delete the anomalies as they interfere with the accuracy of my results, and I will draw the graph again.
This graph shows positive correlation although it is quite weak and not as strong as I expected it to be.
I expected to see this correlation but I thought the correlation would have been stronger.
The Key Stage 2 results are also hard to judge intelligence with as there are only 5 levels a student can fall into (2-6) so the very bright students can only get a level 6 when they could be capable of a level 7, and not so bright students may not even be capable of a level 2, but that is the lowest they can get.
On the whole the graph gives me evidence to say that generally students with a high IQ will perform better in exams than those with lower IQs.
Evaluation
I think that the method I used to do this investigation was quite reliable.
This is because I think I showed my data with appropriate tables and graphs and I think my method of deleting anomalies helped me to improve my proof that exam results are related to IQ.
To increase the accuracy I could have used a larger sample as mine was quite small so my results were limited.
I am now going to extend the investigation and separate the boys and girls and see if there is a difference in the strength of the correlation with gender.
Comparing IQ
These histograms and box and whisker diagrams compare the IQs of the Girls with the IQs of the Boys. They show that a large proportion of both sexes have an average above the national average although the girls average is slightly higher (the boys median is 103.5 and the girls is 107.1). Both sexes have the same range of 80 and the spread on the histogram is basically the same, with the modal class interval 100 < 120 for both sexes. The mean for the girls is 103.3 which I worked out separately in Excel and is over the national average, and the mean for the boys is 98.5 which is under the national average. This suggests that girls in general have higher IQs than boys.
Comparing Key Stage 2 Averages
These histograms and box and whisker diagrams compare the boys and girls KS2 Results. The histograms show me that the Girls and Boys both have the same medial class interval of 4 < 4.5, but the girls have higher results as none of the boys reached the 5 < 5.5 class and a number of the girls did.
The box and whisker diagrams show me that the boys have a lower median (4) than the girls (4.3), and the girls have a slightly higher mean (4.2) worked out separately in Excel) than the boys (4.0).
This scatter diagram of Boys and Girls IQs against average Key Stage 2 results shows that Girls have slightly higher IQs and exam results than Boys as the correlation for the Girls is slightly stronger than the Boys. But this only shows the 60 people that I sampled and this may not be true for the entire population, and there are a few anomalies which decrease the accuracy of the graph.
I will now re-draw the graph without most of the anomalies to improve the accuracy.
This is a scatter diagram showing the boys KS2 results and IQ against the girls. There is strong positive correlation. The graph shows that in general the girls have higher IQs and higher KS2 results than the boys. There were lots of anomalies on this graph though, and many of the boys did in fact get higher results than some of the girls.
Conclusion
Having investigated my hypothesis using stratified sampling, histograms and other suitable data handling diagrams, I can conclude that IQ does affect exam results in such a way that Key Stage 2 results are higher when the IQ of the person taking the exam is higher. This means that Key Stage 2 results are directly proportional to the IQ of the person taking the exam. My graphs on page 5 prove this, as they show this as a general trend, and are backed up by the histograms and box and whisker diagrams on the previous pages.
I can also comment on the IQs and Key Stage 2 results of the students in my sample at Mayfield School.
Many of the students had over average IQs which were reflected in their exam results, as a large proportion of the students my sample had over average means and medians for their results.
The students also have over average Key Stage 2 results. This is shown on my histogram. The mode was also 4.1 which is over the average.
Although I can say this, there are still some students with under average Key Stage 2 results and IQs.
I also investigated the relationship between sex and IQ/KS2 results.
I can say that the girls in general had higher IQs and exam results than the boys. This is shown on my scatter diagram on page 8.
The girls also had a higher median (4.3) and mode (4.2) than the boys did (median – 4.0, mode – 4.0).
This may not be true for the entire population, as I have only looked at my sample.
This is a copy of my sample.
ALYSA EMERY
MATHS COURSEWORK