Then I calculated the amount of samples I would use for year 9. The total population of year 9 is 261 pupils I then found how many females and male, there were 143 females and 118 males. This information I gathered was then put into a calculation to find out how many samples I would use for females and males. First I found the amount of female samples I would use, I did this by dividing the total population of year 9 (261) by the amount of females (143) which gave me a product of 0.55. I then multiplied the total amount of samples by 0.55 which gave me a product of 16.4 which I then rounded to a whole number which gave me a final product of 16 females. After that I found the amount of male samples I would use. The first calculation I conducted was dividing the total population of year 9 (261) by the total population of males (118) which gave me a product of 0.45. I then multiplied the total amount of samples I was using (30) by 0.45 which gave me a product of 13.6 which I then rounded to a whole number which gave e a final product of 14 males.
Finally I calculated the amount of male and female samples I would use for year 11. The total population of year 11 was 170 pupils I then found that there was 86 females and 84 males. After I did that I put the information into a calculation first I calculated the amount of female samples I would use. First I divided the total amount of year 11’s (170) by the total amount of female year 11’s (86) which gave me a product of 0.50. I then multiplied the amount of samples I was using by 0.50 which gave me product of 15.2 which I then rounded up to a whole number which gave me a final product of 15 females. After that I calculated the amount of male samples I would use. I first divided the total amount of pupils in year 11 (170) by the total amount of male pupils in the year (84) which gave me a product 0.50. I then multiplied the amount of samples I was using by 0.50 which gave me a product 14.8 which I then rounded up to a whole number which gave me a final product of 15 males.
The samples I will use
After I had sufficiently completed the sample below are the results that I had obtained. I then typed the results into a Microsoft Excel Spreadsheet. Below is the data that I have gained from my sample. I have decided to only include the Year Group, Forename, Surname, Gender, Height and weight since these is the field, which are important to me whereas other fields are invaluable.
Results from stratified sampling:
Year 7 samples KS3 (key stage three)
Year 9 Samples KS3 (key stage three)
Year 11 samples KS4 (key stage four)
Scatter Graph
I will now produce a number of Scatter Graphs. I will use this to compare the two sets of data when there are two variables, which are height and weight. Also in addition I will use different colours for the dots scattered on the graph to help distinguish males and females this will help with my hypothesis. I will input this data into Microsoft Excel and this will help me produce an efficient and successful graph in which I can then evaluate on the trend.
The scatter graph I have produced shows a very weak positive correlation
between the height and weight of the year 7 students. The graph shows that females on average are slightly taller and weigh more. This graph proves my hypothesis as the students are younger the females are taller and weigh more. But on the other hand I thought that boys would be more active due to certain sports that females do not usually participate in for example football, rugby and boxing therefore the males should weigh less due to doing more exercise. Also due to the amount of people I sampled the data could be unreliable and have anomalies which could have been caused by human error.
The scatter graph I have produced above has a weak positive correlation between the height and weight of year 9 students at mayfields secondary school. The graph shows that the majority of males are taller and weigh more than the females although some females are still taller and heavier than some males. This also proves my hypothesis because this is the age when puberty starts to effect on males and starts to stop effecting females. This is the reason for the males being slightly taller and heavier, also during puberty the males muscles start to develop which in turn will make males heavier.
The graph I have produced above shows a positive correlation between the height and weight of year 11 students from mayfields secondary school. The graph shows the contrast between males and females, you can see that males are much taller and heavier than females. This huge difference is down to the different ways females and males develop to show this huge difference the tallest and heaviest male in the year is 81 kg and 1.92 cm tall and tallest and heaviest female is 65kg and tallest female is 1.80cm. This also is strong evidence in favour of my hypothesis.
Cumulative frequency
I will now produce a number of cumulative frequency graphs to compare the year 7, 9 and 11s. I will use this to compare the two sets of data when there are two variables, which are height and weight. I will try and notice any trends within these graphs that will help me in my investigation.
Lower Quartile= 131
Median= 138
Upper Quartile= 147
Interquartile range= 16
I have noticed that the highest increase was in frequency between {1.4<x<1.5} and {1.5<x<1.6} (22-12=10) and therefore this is the most common height, whereas between {1.1<x<1.2} and {1.2<x<1.3} the difference was 0 (1-1=0) and this was the lowest increase in height and therefore the least common.
Lower Quartile= 36
Median= 40
Upper Quartile= 46
Interquartile range= 10
I have noticed that the highest increase was in frequency between {30<x<40} and {40<x<50} (22-7=15) and therefore this is the most common weight, whereas between {50<x<60} and {60<x<70} the difference was 0 (30-28=2) and this was the lowest increase in weight and therefore the least common.
From my investigation in the year 7 height and weight using cumulative frequency I have found out that the most common height is between 140cm to 150cm and the most common weight is between 40 and 50 kg.
Lower Quartile= 149
Median= 157
Upper Quartile= 164
Interquartile range= 15
I have noticed that the highest increase was in frequency between {1.5<x<1.6} and {1.6<x<1.7} (23-12=11) and therefore this is the most common height, whereas between {1.7<x<1.8} and {1.8<x<1.9} the difference was 1 (30-27=3) and this was the least increase in height and therefore the least common.
Lower Quartile= 39
Median= 45
Upper Quartile= 53
Interquartile range= 14
I have noticed that the highest increase was in frequency between {30<x<40} and {40<x<50} (15-3=12) and therefore this is the most common weight, whereas between {50<x<60} and {60<x<70} the difference was 5 (30-25=5) and this was the least increase in height and therefore the least common.
From my investigation in the year 9 height and weight using cumulative frequency I have found out that the most common height is between 160cm to 170cm and the most common weight is between 50 and 60 kg.
Lower Quartile= 148
Median= 154
Upper Quartile= 166
Interquartile range= 18
I have noticed that the highest increase was in frequency between {1.5<x<1.6} and {1.6<x<1.7} (16-4=12) and therefore this is the most common height, whereas between {1.8<x<1.9} and {1.9<x<2.0} the difference was 1 (30-29=1) and this was the least increase in height and therefore the least common.
Lower Quartile= 37
Median= 42
Upper Quartile= 48
Interquartile range= 11
I have noticed that the highest increase was in frequency between {40<x<50} and {50<x<60} (21-5=16) and therefore this is the most common weight, whereas between {70<x<80} and {80<x<90} the difference was 1 (30-29=1) and this was the least increase in weight and therefore the least common.
From my investigation in the year 11 height and weight using cumulative frequency I have found out that the most common height is between 160cm to 170cm and the most common weight is between 50 and 60 kg.
Evaluation of Hypothesis
In my opinion I feel that my investigation was successful, I believe that the evidence that I have proved successfully was key to my investigation and inevitably I have proved that my prediction was correct. Even though I could not evaluate all the students heights and weight I still believe that the trends that I discovered would be repeated if I extended my sample would be the same. In general I believe my hypothesis was correct.