mayfield high school handling data coursework

 

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I am going to use stem and leaf diagrams because this type of diagram makes it easy for me to find the averages and range for my data this is important because they will help me prove my hypotheses by giving me a spread of my data telling me how consistent my data is it will also tell me whether my is reliable or not.

                         

        

     

                                                       

                 

                                 

                                                         

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For my sample size I decided to select 250 students. I had chosen to use stratified sampling to decide on what pupils to pick for my sample sizes I chose this sampling technique because it take all everyone in the population in to account when I am collecting my sample, Once I had done that to choose my data I simply used a random generator to pick my data by random. For all my calculations I would be using whole numbers because I am using b people and you can’t use parts of people.

To find out how much people I needed for each year divided the number of students in the year by the total students and then times it by the sample size.

Year 7= 282÷1183 × 250= 59.9594= 60 (2 sig fig)

Year 7 girls= 131÷282×60=27.8723=28 (2 sig fig)

Year 7boys = 151÷282×60=32.1276=32(2 sig fig)

Year 8 =270÷1183×250=57.0583=57 (2 sig fig)

Year 8 boys=145÷270×57=30.61111=31=2(sig fig)

Year 8 girls=125÷270×57=26.3888=26=2(sig fig)

Year 9= 261÷1183×250=55.1653=55 (2 sig fig)

Year 9 boys 118÷261×55=24.8654= 25(2 sig fig)

Year 9 girls= 143÷261×55=30.13409=30(2 sig fig)

Year 10=200÷1183×250=42.2654=42= (2 sig fig)

Year 10 boys=106÷200=×42=22.26=22(2 sig fig)

Year 10 girls=94÷200=×42=19.74=20(2 sig fig)

Year 11=170÷1183×250=35.92561285=36(2 sig fig)

Year 11 boys= 84÷170×36=17.7882=18(2 sig fig)

Year 11 girls= 86÷170×36=18.21176=18(2 sig fig)

Table of results

                             

My sample data

Summary table

This is my summary table, here I will give you a summary of my findings in a table which shows all the necessary information. I will be presenting this table because it will help me establish whether my hypotheses were correct according to my findings.

Heights

This table shows me that year 11 boys are averagely taller than any other group however year 11 boys don’t have the most consistent data this means that there data is not as reliable, the group with the most consistent set of heights is year 10 boys this is purely because of the fact that year 10 boys have the smallest range which means they have the most reliable and consistent set of data.

Weights

This table shows me that year 11 boys are averagely heavier than any other group this purely because of the fact that year 11 boys have the highest mean weight, however year 11 boys don’t have the most consistent data this means that there data is not as reliable, the group with the most consistent set of weights is year 10 boys this is purely because of the fact that year 10 boys have the smallest range which means they have the most reliable and consistent set of data.

R squared values

This table shows to me that year 11 boys have the most highest r squared value this means that year 11 boys have the most positive correlation, furthermore this means that as each year 11 boy is getting taller he is also accumulating weight. The group with the lowest r squared value is was the year 9 girls this means that this group has the least correlation from the other groups, possible reasons for this is that this group has the most anomalous results

 

What does this table show me in relation to my hypotheses?

My hypotheses- Main Hypothesis: the taller you are the heavier you are

Sub hypotheses: year 11 boys are heavier than year 9 boys

                           Year 9 girls are taller than year 7 girls

                            Boys are heavier than girls

                           Key stages 4 are heavier than key stage 3

By using this table I have been able to establish that my main hypothesis which states is “the taller you are the heavier you are” is correct I know this because as I look in my table as the average height is going up the average weight is also increasing, sub hypothesis 1 which states: “year 11 boys are heavier than year 9 boys” is correct I know this because the mean weight of the year 11 boys is greater than the mean weight of the year 9 boys, also my findings prove my sub hypothesis 2 which states “Year 9 girls are taller than year 7 girls”

I know this because the average height of year 9 girls is greater than the average height of the year 7 girls, however whether my third sub hypothesis which states “Boys are heavier than girls” is proved is questionable because in all the years except year 8 the boys are averagely heavier but this is not the fact in year 8. For my fourth sub hypothesis which states “key stage 4 are heavier than key stage 3” I have established that it is correct I know this because the average of the two key stage 4 groups (boys and girls) are both heavier than any other group from key stage 3.

Conclusions

By doing completing this investigation, I have come to a conclusion to the following things:

• The taller the student attending Mayfield high school are the heavier they are  I know this because as I look in my table as the average height is going up the average weight is also increasing.
• Year 11 boys attending Mayfield high school are heavier than year 9 boys I know this because the average weight of the year 11 boys is 63.3 KG which is greater than the mean weight of the year 9 boys which is 51.7 KG.
• Year 9 girls attending Mayfield high school are taller than year 7 girls attending Mayfield high school I know this because the average height of year 9 girls is 1.61 which is greater than the average height of the year 7 girls which is 1.55.
• key stage 4 students attending Mayfield high school are heavier than key stage 3 students attending Mayfield high school  I know this because the average of the students key stage 4 are  heavier than any students from key stage 3.

Despite me proving all these statements I was still unable to prove one of my statements this statement was Boys attending Mayfield high school are heavier than girls attending Mayfield high school this was no proved because in all the years except year 8 the boys are averagely heavier but this is not the fact in year 8. Me not proving this hypothesis could of been because of me underestimating the students of the school.

Evaluation

Despite me proving the majority of my hypotheses, I still feel that my results could be inaccurate, possible things that could have contributed towards my inaccuracies are;

• A systematic error occurring because of me for example me selecting an extra student for my sample.
• Me using the incorrect graph to prove my hypotheses for example I would need to make a scatter graph to compare 2 years heights and weights but I use a line graph.
• Another thing that could of resulted in inaccuracies in my data could be my degree of accuracy I think this because my degree of accuracy could affect one value more than another e.g. to 3 significant figures would be more appropriate to a number in whole number e.g. weight but it would give 1 decimal place after the units.

In future if I were to do this investigation again I would make these changes to my methods and my techniques because it would make my enquiry more accurate and precise;

• I would have a bigger sample size of 300 I would use this sample size because I feel that this size would give me more accurate results compared to my sample size of 250.
• Another technique I would use if I was to do this again would be to pick my students with normal random sampling as opposed to a random generator i would do this because I personally would find it more easier.
• I would also use histograms in my enquiry if I was to do it again I would use a histogram because it would give me a better visual representation of the patterns within my data.
•  I would also think about my degree of accuracy in more depth whilst thinking about the possible numbers that could appear and what degree of accuracy they would need.