Handling Data - Mayfield High School

Authors Avatar
GCSE Mathematics Coursework

Handling Data - Mayfield High School

Key Stage 2 results at Mayfield School

The Plan

I am investigating the factors that affect Key Stage 2 results. Factors that may affect Key Stage 2 results are:

IQ If someone is intelligent they are more likely to get good Key Stage 2 results

Primary school The standard of education at different primary schools varies so the understanding of subjects of different pupils is likely to be affected by their primary schools'.

Age The older pupils in a year, those whose birthday is in September, may have acquired a better understanding in their subjects due to their brains being more fully developed whereas younger students in a year, those whose birthday is in August, will be at more of a disadvantage concerning Key Stage 2 results as their minds will not be as developed as those older than them.

Year group New teaching methods, such as the Numeracy Hour, have been introduced since older years, such as years 10 and 11, have been educated and so the younger years, for example years 7 and 8, may have benefited from these new teaching methods and have a better understanding of their subjects therefore are more likely to get better Key Stage 2 results.

Gender It is said that in general girls cope better in exam conditions than boys and so are more likely to get better Key Stage 2 results.

I cannot investigate how different primary schools and how new teaching methods, such as the Numeracy Hour, affect the students' Key Stage 2 results as I do not have the data to support this.

I am going to investigate how IQ and gender affect Key Stage 2 results.

Hypothesis 1: There is a strong positive correlation between IQ and Key Stage 2 results.

Hypothesis 2: (a) IQ of boys and girls is normally distributed, in line with national ....figures.

(b) Gender makes no difference to IQ.

Hypothesis 3: Key stage 2 results are not influenced by gender.

The data I have is secondary, collected by a school I do not know so I am not sure if this data is reliable or not. I am not going to use any obvious anomalous data.

Hypothesis 1

I am going to take a stratified sample of the whole school to find out if there is a strong positive correlation between IQ and Key Stage 2 results. I am using a stratified sample so that it is a fair representative of the data as there may be different numbers of students in each year. I am using a sample of 50 students, as the sample won't be too small or too big so the data will be reliable but manageable. I will also have enough data to make a clear scatter graph, 50 points on a scatter graph will be enough to provide proof of whether there is strong correlation or not. Using more data would only waste time as it would not help to prove the strength of my results. The table below shows the numbers of students of each year and gender.

Year

Number of boys

Number of girls

Total number of students in year

7

51

31

282

8

45

25

270

9

18

42

260

0

06

94

200

1

84

86

70

Total number of students at school:

182

The next table shows how many students I will choose from each category in my stratified sample and how I worked this out.

Year

Number of boys

Number of boys I will use in sample:

Number of boys

Total number of x 50

students

Number of girls

Number of girls I will use in sample:

Number of girls

Total number of x 50

students

7

51

(151/1182)*50 = 6

31

(131/1182)*50 = 6

8

45

(145/1182)*50 = 6

25

(125/1182)*50 = 5

9

18

(118/1182)*50 = 5

42

(142/1182)*50 = 6

0

06

(106/1182)*50 = 4

94

(94/1182)*50 = 4

1

84

(84/1182)*50 = 4

86

(86/1182)*50 = 4

Total number of students in sample:

50

This sample will be random so every student in the sample has an equal chance of being picked so there is a fair representative of data. To get my random sample I shall use the random number function on my calculator.

Once I have my stratified sample I will plot a scatter graph showing Key Stage 2 results (y axis) against IQ (x axis). I will divide the graph into quadrants which will help me to decide whether there is strong positive correlation between IQ and Key Stage 2 results or not. If there is strong positive correlation I am going to draw a line of best fit on this graph and I will find its equation, which will further show the relationship between IQ and Key Stage 2 results.

Hypothesis 2a

To investigate whether the IQ of boys and girls is normally distributed, in line with national figures, I am going to collect a different stratified sample of 50 girls and 50 boys from year 8. I will collect my sample using the random number function on my calculator.

My main reason for testing this hypothesis is to check the validity of my results. I know from the internet that across Britain IQ is normally distributed with mean 100 and standard deviation 15. If I find that this is also true for year 8 pupils at Mayfield then this will be good evidence that any results I have from my hypotheses are likely to be true across Britain and not just this school. For example I might have to change hypothesis 1 to "At Mayfield School there is strong positive correlation between IQ and Key Stage 2 results.
Join now!


I shall group the IQ of boys and draw a histogram. I shall need to draw a histogram because the class-widths will not be equal. I will then join the midpoints of each class-width on the histogram with a curve. If the curve is more or less symmetrical, 'bell-shaped', the data is normally distributed.

I shall calculate the mean and standard deviation for boys' IQ, and then I will find whether the IQ of boys is normally distributed by finding if 68% of the data lies within 1 standard deviation of the mean, and 95% of the ...

This is a preview of the whole essay