# My hypotheses are: -1. People's average SAT and average GCSE results will have a strong positive correlation between them.2. Girl's average GCSE result will generally be higher than boy's average GCSE result.

The Plan

My hypotheses are: -

1. People’s average SAT and average GCSE results will have a strong positive correlation between them.
2. 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.

...