GCSE Mathematics Jaitej Walia 10K

Statistics Coursework 8 November 2008

GCSE Mathematics Statistics Coursework

A. Introduction

My Task is about intelligence. The questions that I am going to investigate are:

1. -The mean of boys and girls in SATS scores.

-The area/frequency of boy’s and girls SATS score.

2. -The correlation and relationships between the IQ of Year 7 Boys and Girls, Year 11 Boys and Girls; and also the SATS scores of Year 7 and 11 Boys and Girls.

-What happens to the frequencies as the IQ and SATS scores goes higher?

B. Hypotheses

The hypotheses I will be testing are whether

-Boys do better in SATS than girls

- The higher the IQ, the higher the average SATS score.

I think that these hypotheses are true as boys, historically, have a better mean than girls, and if you are more intelligent than someone, (calculating from your IQ), you will do better in your SATS.

C. Plan of Action – Data Collection

I will need to collect the data from Mayfield High School. The data I will need to collect are “Year 7’s boys; Year 7 girls; Year 11 boys; Year 11 girls” data. This data will be useful as I can use and explain a wide range of data from both genders and I can conclude the intelligence of elder and younger pupils. I will only collect a little data from each data group e.g. 20 pupil’s data from the “Year 11 girls” data group. I will need to take a sample from the population, as it’ll be quick as well, instead of using the whole population’s data. I will take a stratified sample as this is a fair method, and it isn’t biased as it is random. I will be using secondary data, as I am going to take data from another source. I will get my data from Mayfield High School which is a fictitious school however; the data presented is based from a real school. This data has been stored on a computerised data base where I can get a large quantity of data, and the data is easy to find. However, the accuracy of the data may not be known.

My data will be reliable and not biased as I will use stratified sampling for each data group. I will only have some qualitive data, such as the names of pupils, however this will not effect my conclusion, whether these qualitive data are different. I will use quantitive data which include numbers e.g. IQ and Average SATS score. My quantitive data will be continuous as I will be comparing two variables, using scatter diagrams, for my second hypothesis. However, I will also be using discrete data as I will need to find an average using mean, median and range, which will develop into using box plots and eventually using cumulative frequency to compare one variable, which is continuous data, but using one variable will also help me get my answer for my first hypothesis.

I will record my data on a spreadsheet which involves using macros and sampling in a stratified way, and a calculator to put my answers into the computer. The only problem I will expect to have is a typing error in my calculator but I will have to be careful in typing in the correct calculations to get the right answer. I could also double check the answer when typing.

D. Plan of Action – Processing and Representing Data

I will need to group my data by grouping each data in each year group and gender in a field e.g. Year 7 Boys; Year 7 Girls; Year 11 Boys; Year 11 Girls. For each incorrect or incomplete data, I will use it as an outlier, displaying it with a box plot.

I am going to create data tables of many samples to show the differences of different samples and groups. I am going to use stratified sampling as statistical calculations. I am going to take a sample from the population of Year 7 Boys. I will take the number of people, divided by Total number of people at the school, times by the sample size. e.g.

For Year 7 Boys it will be: 151 / 1183 x 200 = 26

For Year 7 Girls it will be: 131 / 1183 x 200 = 22

For Year 11 Boys it will be: 84 / 1183 x 200 = 14

For Year 11 Girls it will be: 86 / 1183 x 200 = 15

I hope the results of my calculations will give me the correct and relevant data. For hypothesis 1, I will use Autograph 3.2 (a software package) to calculate the area and frequencies of Boys and Girls Average SATS scores using histograms. I will calculate standard deviation using a calculator and the formula is shown on the next page:

For grouped data, I will use another method for standard deviation, and the formula for it is shown below:

For hypothesis 2, I will use Autograph 3.2 as well, and calculate the cumulative frequency of the IQ and Average SATS scores of Year 7 and 11 Boys and girls; and then create box plots, to show the mean, median, lower and upper quartile range. I will also use scatter diagrams to show me the relationships between IQ and Average SATS scores, and also show me the Spearmans rank correlation coefficient. The formula I will use for Spearmans rank correlation coefficient is:

Year 7 Boys

This table has the relevant and important pieces of data of 26 random Year 7 boys, which will be used in diagrams, charts, graphs and calculations to find the answers to my questions and to provide information for my original hypotheses.

Year 7 Girls

This table has the relevant and important pieces of data of 22 random Year 7 girls, which will be used in diagrams, charts, graphs and calculations to find the answers to my questions and to provide information for my original hypotheses.

Year 11 Boys