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  • Level: GCSE
  • Subject: Maths
  • Word count: 2043

This coursework is about a statistical analysis to investigate the height and weight of pupils within Mayfield High School

Extracts from this document...

Introduction

image00.png

Introduction

This coursework is about a statistical analysis to investigate the height and weight of pupils within Mayfield High School. The total number of pupils in the school is 1183 but I don’t have time to collect all the heights and weights of all the students so I obtained a random stratified sample of 200 students. I acquired this random stratified sample of 200 pupils by calculating the percentage of male and female in each year group and used the data to form the proportion of students I would take in the sample from each year group. When I attained the percentages of each year group I found that I had to round them up so I could get the whole numbers of pupils instead of having half a pupil and three-quarters, for example, I had to round up 10.6% to 11%, but in the end I still made it up to 100%.

The working out looked like this:

Yr

Gender

Pupils

Percentage for 200

Proportional Sample

7

f

131

11%

22

8

f

125

11%

22

9

f

144

12%

24

10

f

94

8%

16

11

f

86

7%

14

f

Tot. 579

49%

98

7

m

151

13%

26

8

m

145

12%

24

9

m

117

10%

20

10

m

106

9%

18

11

m

84

7%

14

m

Tot. 604

51%

102

M and F

Tot. 1183

100%

200

In selecting my data I found that there were errors in the database e.g. I found 3 female students in year 7 all weighing between 110kg and 140kg and I also found that there were 4 students weighing under 10kg – lighter than a sack of rice. image01.png

image26.png

I also found some outrageous heights.

image27.png

Hypotheses

  1. As height increases, weight increases
  2. Boys are naturally taller that girls
...read more.

Middle

image24.pngimage23.png

Fig 1.4

From what I have read, predictions are probably even better if we separate the genders so this is what I will do next.


Data separated for Girls and Boys

I will use the same process that is, enter data and used the program Autograph to plot a scatter graph.

These are my results for girls.

image52.png

For the correlation coefficient of this data, I used the function button in Excel.

image53.pngimage25.png

These are my results for boys.

image54.png

image28.pngimage02.png

Perhaps to get a better correlation coefficient the data also needs to be separated by age.

Data in groups: yr 7 and 11, separated for Girls and Boys

Year 7 girls.

image29.pngimage03.png

Year 7 boys.

image30.pngimage04.png

My response to hypothesis 1, that weight increases as height increases is that, it is true. However, the correlation

Coefficient shows that the relationship is variable between the sexes and for individual age groups. I am not going to go any further in this line of exploration because the data is so unpredictable and it’s driving me insane.

But I will look at the average height of the boys and girls.


Boys are naturally taller than girls

I believe that boys are naturally taller than girl so I will conduct tests to see whether my hypothesis is right or not. I will first get the averages for all the boy/girls in each year by obtaining the total heights and then dividing it by the number of pupils.

...read more.

Conclusion

image45.png

Using excel I worked out percentages and entered them onto the autograph data sheet.

image46.png

There are still more boys who are 1.56 metres or less than there are girls. The heights of boys’ fall into a smaller range than the height of the girls’. As this range is probably important I am going to compare the distribution of heights once again but this time using box and whisker diagrams.

image47.png

It box and whisker diagram shows that girls (yellow) have both a wider range and wider inter-quartile range of heights than do the boys (blue). The advantage of the box and whisker diagram is that it deals with sample proportions (quarters/quartiles). It doesn’t matter how big or small each sample is.


Now that I know that boys are taller than girls I can now predict that boys are heavier than girls so I will make a table and find the mean for them to see if I am right.

Female Year

Total Weight

No. pupils in year

Average

7

978

22

44.455

8

1072

22

48.727

9

1274

24

53.083

10

747

16

46.688

11

632

14

45.143

Male Year

Total Weight

No. pupils in year

Average

7

1124.5

26

43.25

8

1072

24

44.667

9

1012

20

50.6

10

988

18

54.889

11

869

14

62.071

From this data I am sadly mistaken and I now see that girls are heavier than boy from year 7-9 but after that boys are heavier than girls. So over all girls are heavier than boys for a certain point but boys are heavier in the long-run.


As age increases, the rate of growth decreases

...read more.

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