The Plan

My hypotheses are: -

- People’s average SAT and average GCSE results will have a strong positive correlation between them.
- Girl’s average GCSE result will generally be higher than boy’s average GCSE result.

All the data used will be from Steel City School

For both of my hypotheses I am going to use a sample of 55 people. For my sampling I am first going to use stratified sampling, when I have a number of people I am going to role a dice to decide where I start. I believe that the minimum number of people that should be sampled is 50. 50 out of the 166 pieces of data is 30% and 55 out of 166 is 33%. With only 30 pieces of data in my sample I believe that I may not get a good spread of both boys and girls results. With a sample of 55 I believe that I will get a fair sample and a large spread of both boys and girls.

I intend to show the data on a series of graphs. For my first hypothesis “People’s average SAT and average GCSE results will have a strong positive correlation between them.” I am going to use three scatter graphs. The first graph will be a scatter graph showing only boys average SAT and GCSE results. The second graph will be a scatter graph showing only girls average SAT and GCSE results. The third and final graph will show both boys and girls average SAT and GCSE results. On all three I will plot a line of best fit. I am also going to use Spearmans Co-efficient of Rank Correlation to help prove whether or not there is a strong correlation between average SAT and GCSE results.

For my second hypothesis “Girl’s average GCSE result will generally be higher than boy’s average GCSE result.” I am going to use two cumulative frequency graphs. The first graph will be a cumulative frequency graph showing only boys average GCSE results. The second graph will be a cumulative frequency graph showing only girls average GCSE results. On these graphs I will plot a line of best-fit, upper and lower quartiles, inter-quartile ranges, box plots and a median point. I am also going to draw one histogram, on this histogram I am going to plot both boys and girls average GCSE result as a percentage. I am also going to draw three labeled pie charts. The first pie chart will be a pie chart showing only boys average GCSE results. The second pie chart will be a pie chart showing only girls average GCSE results. The third and final pie chart will show both boys and girls average GCSE results.

Hypothesis One

As I stated in my plan I am going to use stratified sampling of 55 people. There are 167 pieces of data but I have not included the 167th piece of data because it does not specify whether it is for a boy or girl, it also does not contain any data apart from the total score and the average score of the GCSE results. This means that I have counted 75 boys and 92 girls with the 167th piece of data not being used I have now got 91 girls. Below I will show how I have done this.

## Boys

(75 166) 55 = 24.8493975903614457831325301204819

24.8 (1DP)

I have decided to round up the 24.8 to 25 so that I have a whole amount of people to use.

To find out how large or small the difference is I have done 75 25 this equals 3. This means that the person that I am going to pick is every third person. To find out whether I start on the first, second or third person I rolled a dice. This dice landed on a three so the first piece of data is the third.

## Girls

(91 166) 60 = 32.891566265060240963855421686747

32.9 (1DP)

I have decided to round up the 32.9 to 33 so that I have a whole amount of people to use.

To find out how large or small the difference is I have done 91 33 this equals 2.75. Again I have rounded this up. This time it has been rounded to 3. This means that the person that I am going to pick is every third person. To find out whether I start on the first, second or third person I rolled a dice. This dice landed on a three so the first piece of data is the third.