Reasons for choosing source of information
The main reason why I choose to look at Mayfield High School is because; the data within the booklet is accurate as it is the results of carefully prepared and planned tests, so therefore the results will be very accurate. Also, as the information are based on examinations enforced by the government – the results are more likely to be reliable than that of class tests.
The variables that I will be looking at are based on abilities. The measurements of ability can be quite tedious as there is more than one way of measuring abilities. However, from general knowledge, I know that the formal examinations set by the examinations board are not some questions written overnight, but more so questions that have been specially selected and worded in a way to attain the best indicator of ability. Thus, the source of data is highly accurate.
Reliability/Accuracy of variables
The most accurate analysis of data that I will obtain is the KS2 level 2 results that students achieved. This is because; only 17 people achieved level 2 and my sample consists of only 15 students per KS2 level, as you can see my sample covers almost everyone that achieved a level 2. This makes my findings very reliable.
The least accurate finding would have to be of students that achieved a KS2 level 4. This is because nearly half of Mayfield High School achieved KS2 level 4 – 552 students to be in fact. Because there are a huge number of students that achieved a level 4, it could show different trends achievements within that variable. However, my findings won’t be unreliable as my research will still find a trend for students achieving a KS2 level 4 – but more so that the trend I will discover won’t necessarily reflect everyone that achieved a KS2 level 4.
In my variables, the calculator randomly selected a student number that did not match its IQ number with its KS2 result number; therefore I decided to discard that reading as it could be a printing or a typing error.
Sampling
There are very different types of samples used to find out different information.
A SELECTIVE sample is one which every nth term is chosen, where n is selected at random e.g. taking every 10th piece of data.
A STRATIFIED sample is one which the population is divided into groups called strata and each stratum is randomly selected.
A RANDOM sample is one in which each member of the population is equally likely to be selected.
I will use a RANDOM sample; this is because I want every student in Mayfield High School to have an equal chance to be selected.
The initial sample that I will use to look at is 15 students, regardless of gender, from each KS2 results. In order for me to do this, I used the random button on my scientific calculator to get random numbers of students. The calculation I used was: Total number of students to be sampled × SHIFT Ran# = Keep pressing the = button to get another random number.
Recording the Data
Below are the randomly selected students with their IQs:
Below shows the Frequency and the Cumulative Frequency table of the IQs:
I used a table to record the IQs of all the KS2 results, I then calculated and conducted a cumulative frequency table. Afterwards, I used my data to plot cumulative graphs to find out accurately the Lower-Quartile, Upper quartile, Inter-Quartile Range and the Median. In the end, I drew box and whisker plots on one scale so I could easily analyse the data.
The tables show the IQs for each KS2 results, the mean is the weighted average and is worked out by the sum of frequency multiplied by the mid points of each class. The formula is ?fx divided by the sum of all the frequencies.
Analysis
Level 2
The lowest IQ needed to attain a level 2 is 60 and the highest IQ for level 2 is 120 - this gives it a very wide range of 60, however, I don’t want to look at the extreme values, so therefore, it is sensible to have fewer extreme values. To enable me to have an accurate spread of the students who achieved level 2, I will find the difference between the lower-quartile and the upper-quartile. So, the inter-quartile range for students who achieved a level 2 is 15.25 – the median IQ value in level 2 is 74.
Level 3
The lowest IQ needed to get a level 3 is 70, just 10 more than level 2. The range for the entire spread of level 3 is 8.9 – this is actually quite small. More than half of the sample I chose had an IQ between 90 and 99, 8 to be precise. What is odd is that the highest IQ of level 3 is actually lower than the highest IQ of level 2; this suggests that probably the students in level 3 are working harder and that students in level 2 are working less hard as they have high IQs but are on a lower KS2 grade. The median IQ for level 3 is 95.2
Level 4
Looking at the box and whisker plot, the box looks very ‘uniform’ like, each section of the box look equally distributed – suggesting that students in level 4 are on target, it also suggests that all students are achieving what they need to achieve and that level 4 is the most achieving in the KS2 grade. The lowest IQ needed to get level 4 is 90; 20 more than level 3’s lowest IQ. The inter-quartile range is 10 which is quite big. The highest IQ for level 4 is exactly the same as level 3, 110 - this states that level 3 and level 4 students have the same highest IQ which in turn is suggesting that level 4 students aren’t working as hard as they can as they are getting the same highest IQ as level 3. The median IQ for level 4 is 100.5
Level 5
The lowest IQ needed to get a level 5 is the exact same as the lowest IQ for level 6 - this alludes to the fact that either level 5 students are working very hard or that level 6 students aren’t working hard enough, the debate can be argued from both viewpoints. The inter-quartile range for the spread is 11.4 – the highest IQ for level 5 is 116.4 which is less than level 6’s highest IQ, this shows that logically students need a higher IQ to reach level 6. On the box and whisker plot scale, it can be seen that just like level 3 and level 4 IQs, level 5 and level 6 students have similar IQs.
Level 6
The lowest IQ needed to get a level 6 is 100 and highest IQ value is 140. The inter-quartile range is 12.5. On the CF graphs, the IQs needed for level 6 is an almost perfect curve, this tells us that the students have an equally distributed balanced range between 100 and 140. All in all, I’m guessing level 6 students are working very hard as most of the students are on IQs between 111 and 123.5. However, what is striking is that, a person with a level 6 capable IQ, 120, is on level 2, while another individual in level 6 has the exact same IQ. An explanation for this is that the individual in level 2 with a very high IQ is intelligent but there are obstacles that don’t allow them to be in level 6; these could include: the student was probably disruptive, the student didn’t revise probably for their exam or maybe they don’t like Math.
Conclusion
I will now see if my hypotheses were correct. The first one: as the IQ increases the KS2 result for will also increase. My findings show that generally, the trend is that as the IQ increases the KS2 results increase too. My first hypothesis was correct (there are few exceptions). The second hypothesis: students who have low IQs will have a lower KS2 result. Again, my hypothesis was correct as the students with low IQs had low KS2 level. Finally, the third hypothesis: students who have low IQs but work hard will have higher KS2 results than students who have high IQs; I believe this is incorrect. My third hypothesis is wrong. My findings suggest that students who have low IQs tend to have lower KS2 results. This is the general trend, however, there is a minor trend that hard-working students with low IQs have high KS2 results.
Extension: 1
Stating the Task and writing a Plan
Introduction
As part of my extension, I am going to look at which gender is outpacing the other in three different year groups throughout secondary schooling. To do this, I will look at three stages of secondary education, hence Year 7, Year 9 and Year 11.
Hypothesis
I think girls will outpace boys all the way throughout secondary school.
I predict that, boys will underachieve throughout secondary school.
I predict that girls will start the beginning of secondary school with better IQs than boys.
My hypotheses are influenced by what I studied in Sociology. The ‘Social Trends Pocketbook 1999’ highlighted that both boys and girls were doing better at school than they used to, but they also showed that girls are overtaking boys at secondary school, between 16-19 and catching up fast at degree level.
Some suggestions to why girls outperform boys are to do with the attitudes each gender show towards education and life. Generally, boys will show a ‘laddish anti-learning culture’, otherwise, they’re scared of being picked on by other boys. While, on the other hand, girls are willingly to spend more time doing , not rushing it. You can see that logically speaking, girls should outperform boys.
Sampling
I am going to use a sampling frame of 24 people. The type of sample I am going to use is a stratified sample. A stratified sample is when the sample frame can be divided into two groups. I am choosing to do 12 boys and 12 girls, the sample of gender are equally likely to be chosen as they are selected randomly.
Reliability/Accuracy
All the students IQs are chosen randomly by the calculator, thus, my findings are reliable. Also, because I used a very large scale on the Cumulative Graphs, it meant that the accuracy of the Lower-Quartile, Upper quartile, and Median increases. One thing I changed from my original CF graphs was instead of hand drawn curves I used a ruler to join the crosses together, this too increased the accuracy of the Lower-Quartile, Upper quartile, and the Median.
Recording the data
I used a table to record the IQs of boys and girls from each year groups, I then calculated and conducted a cumulative frequency table. Afterwards, I used my data to plot cumulative graphs to find out accurately the Lower-Quartile, Upper quartile, Inter-Quartile Range and the Median. In the end, I drew box and whisker plots on one scale so I could easily analyse the data.
Below are the Tally tables for the data handling:
Analysis
Year 7
In Year 7, as expected, girls had an overall higher IQs. The lower bound and the upper bound were higher for girls that boys as well as the median. The average IQ for boys in Year 7 is 87.1, whereas, girls have an average IQ of 94.3 – a difference of 7.2; for the Lower-Quartile, Upper quartile, Inter-Quartile Range and Median. Look at the table in the ‘Recording the data’ section.
Year 9
During Year 9, the are in progress, therefore, it is important that both gender do well in their exams. From the box and whisker plots, we can see that boys have dramatically outpaced girls in their IQs. Whilst, girls are being outpaced by boys, this could be because some girls have lots of responsibilities at home whereas boys tend to have more free-time.
Year 11
Year 11 is the most important year for pupils as their GCSE grades partially determines their future. What’s interesting to note is that boys are still out out-performing girls, the difference of the lower bound IQs between boys and girls are the highest difference out of all three year groups, a difference of eight. At the end of secondary, it can be seen that boys are leaving with better IQs than girls – they have more opportunities if they used they’re high IQs to get good GCSE grades.
Conclusion
At the beginning of , girls start off with better IQs than boys. Nevertheless, throughout secondary school, boys are consistently outpacing girls until the end of . One should also not overlook the fact that neither gender are underachieving, they’re both getting better IQs than their previous years, it’s just that boys are doing a bit better than girls.
My first hypothesis: girls will do better is proved to be incorrect. Boys outpaced girls in each year groups (excluding Year 7). My second hypothesis: that boys will underachieve during secondary school, also proved to be wrong. Boys increased their IQs from their previous year group which shows that they are actually achieving their potential, if they had same IQs throughout secondary school then they would be underachieving.
Extension: 2
Stating the Task and a Plan
Introduction
I will look at which gender, boys or girls, are doing better at KS2 level 5 in Year 11. To do this, I will look at the IQs for both genders.
Hypothesis
From my previous extension, I have learnt that overall, boys will have better IQs in Year 11 than girls, therefore I predict that:
Boys will do better in KS2 level 5 in Year 11
Sampling
This is a stratified sample. I wanted to get the whole of KS2 level 5 in Year 11, as there were only 40 and my sample frame consisted of only 30 people. I used this calculation to calculate the stratified amount of boys and girls.
There are 40 students on level 5, 16 students are boys and 24 students are boys.
To find the percentage of gender in level 5 in Year 11 we have to:
Reliability/Accuracy
The above calculations mean that the sample is accurately selected. The random selection of students by the means that the data is reliable. Also, my CF graphs are quite large to give accurate reading of Lower-Quartile, Upper quartile, Inter-Quartile Range and Median.
Recording the data
I used a table to record the IQs of boys and girls from KS2 level 5 results, I then calculated and conducted a cumulative frequency table. Afterwards, I used my data to plot cumulative graphs to find out accurately the Lower-Quartile, Upper quartile, Inter-Quartile Range and the Median. In the end, I drew box and whisker plots on one scale so I could easily analyse the data.
Analysis
Overall, girls had a lower lower-bound of 95, a lower lower-quartile of 102.5, a lower median of 106.25, a lower upper-quartile of 110, a lower upper-bound 0f 121 and a lower mean of 107.1. Basically, we can see that there is a consistent pattern of boys doing better at all the factors of data handling.
Conclusion
My hypothesis was correct; I predicted that boys will do better. One reason why my hypothesis is correct is because I used my knowledge of my first extension to influence my hypothesis. This extension suggests that boys are really doing better than girls and outpacing them. However, it doesn’t mean that all boys around the country are doing better than girls in secondary; we’re just looking at on e school so we can’t assume that my findings somehow portray the performance of genders in schools.
Evaluation
I think I found sufficient information from Mayfield High School to deduct that boys are doing better. One reason why this assignment was quite easy was because I did a similar project for my Sociology coursework, thus, I applied my previous knowledge to this assignment. However, one thing that confused me was how to calculate the stratified sample, in Sociology, when I studied types of samples, we had slightly different meanings - so I was a bit lost in this section.
If I had to do this project again, I would use histograms and present my findings much neater. Due to insufficient time and lack of knowledge on how to do graphs on Microsoft excel limited the creativity of my work.
On the whole, at first I was confused about this assignment but then as I started working on it, the project made sense and I began to get the hand of it.
