• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  21. 21
    21
  22. 22
    22
  23. 23
    23
  24. 24
    24
  25. 25
    25
  26. 26
    26
  27. 27
    27
  28. 28
    28
  29. 29
    29
  30. 30
    30
  31. 31
    31
  32. 32
    32
  • Level: GCSE
  • Subject: Maths
  • Word count: 5617

In this coursework I want to find out what the average height, weight, and arm span of a Year 11 pupil is

Extracts from this document...

Introduction

Philip Davies 11B8th February 2005

The Average Year 11 Pupil

Hypothesis

   In this coursework I want to find out what the average height, weight, and arm span of a Year 11 pupil is. I think that my height, and arm span will be 10% more than the average Year 11 pupil, and my weight will be 5% more than the average year 11 Pupil, I want to find out if this is correct. I will also compare the height, weight, and arm span of an average Year 11 male to an average Year 11 female, because I think that an average Year 11 male will be 10% taller, heavier, and have a 10% longer arm span than an average Year 11 female. Finally, I want to find out if an average Year 11 pupil is square, and if an average Year 11 male is squarer than an average Year 11 female. The calculations and graphs that I am going to make are;

  • Histogram
  • Interquartile Range
  • Mean
  • Box & Whisker
  • Mode (Modal Group)
  • Standard Deviation
  • Cumulative Frequency Graph
  • Scatter Diagram
  • Median

   Each pupil in Year 11 measured their own height, weight, and arm span, and all the data was collected and put in a table. So the data we are using is Primary Data because we have collected it. The sampling which I used to get my data was systematic sampling. To get better results I left out any sets of data with missing measurements. I chose every 4th set of data and recorded it in a table. I decided to choose 25 male, and 25 female sets of data, so I will have 50 sets of data. Here is the data that I have selected;

Gender

Height (cm)

Arm Span (cm)

Weight (kg)

M

187

187

76

M

169

165

55

M

186.4

165

73

M

176

170

57

M

183.5

195

64

M

183

182

65

M

174.5

160

76

M

177.5

176

59

M

180

185

65

M

155

162

46

M

189

200

97

M

178

177

78

M

176.5

175

70

M

165

170

47

M

180

184

58

M

164

164

55

M

182.5

178

92

M

166

168

52

M

172

179

91

M

172.5

168

76

M

180

179

65

M

178

163

65

M

169

167

63.5

M

185

185

64

M

172

175

60

F

163

151

52

F

181

181

65

F

157

163

53

F

160

155

43

F

165

160

70

F

156.5

162

42

F

172

172

62.5

F

167

162

51

F

165

159

50

F

166.7

171

70

F

161

159

60

F

167

168

69.5

F

165.5

170

70

F

164

167

60

F

164

170

65

F

163

155

53

F

162.5

147

60

F

172

165

64.5

F

167

170

65

F

156

165

57

F

157

155

59

F

152

155

47

F

160

166

58.5

F

161

160

58

F

165

165

55

   Here are my measurements;

Gender

Height (cm)

Arm Span (cm)

Weight (kg)

M

182

185

68

   There are no sets of data in the table which stand out, so I believe the data is all genuine. The data that I have collected is Continuous data so I will have to group my data for the 3 measurements.

1.Height (All data)

   I will now do all my calculations and graphs for Height. I will firstly do the calculations and graphs for all of my data, and then I will split the data into male and female and complete the calculations and graphs for them. Here is my table of grouped data for height, including all my data;

Height (cm)

Frequency

150 ≤ h < 155

1

155 ≤ h < 160

5

160 ≤ h < 165

10

165 ≤ h < 170

12

170 ≤ h < 175

6

175 ≤ h < 180

5

180 ≤ h < 185

7

185 ≤ h < 190

4

1.Histogram

image00.png

   From the Histogram above I can see that there are more pupils with a smaller height than pupils with a larger height. I can also see that there is a slight negative skew in the Histogram which shows that there is a bigger distribution of smaller pupils in Year 11.

2.Mean

     Mean =         Sum of Height  =        8491.6  =  169.832cm

                 No. of Pupils           50

   Compared to my height of 182cm, the mean height for Year 11 pupils is 169.832cm, which would make me above average height by 12.1cm. As a percentage this would mean I am 6.6% taller than the mean height of a Year 11 pupil, so my hypothesis was almost correct.

3.Mode (Modal Group)

     Mode (Modal Group) = 165 ≤ h < 170 cm

   The modal group height for a Year 11 pupil is 165 ≤ h < 170 which is

17cm < h ≤ 12cm smaller than my height which means I am 9.3% ≤ h < 6.6% taller than the average Year 11 pupil.

4.Cumulative Frequency Graph

   Here is the table and graph for Cumulative Frequency;

Height (cm)

Frequency

Cumulative Frequency

150 ≤ h < 155

1

1

155 ≤ h < 160

5

6

160 ≤ h < 165

10

16

165 ≤ h < 170

12

28

170 ≤ h < 175

6

34

175 ≤ h < 180

5

39

180 ≤ h < 185

7

46

185 ≤ h < 190

4

50

image01.png

   From the Cumulative Frequency graph above I can see that the gradient of the curve is steeper below the median height, and that the gradient is not as steep for the taller people above the median. This shows that the heights of the smaller pupils seem to be closer together, and the heights of the taller people seem to be more spread out.

5.Median

     Median = 169cm

   The median height of a Year 11 pupil is 169cm, this is 13cm (7.1%) smaller than my height. This shows my prediction of 10% is almost correct.

6.Interquartile Range

     Interquartile Range   =   Q3 – Q1   =   178cm – 163cm   =   15cm

image12.png

   From this diagram and the Interquartile Range I can see that the middle 50% of the data covers almost exactly half of the total data range, so it has got a normal spread. I can also see that the lower 50% of the data is closer together, and the higher 50% of the data is more spread out.

7.Standard Deviation

     Standard Deviation = 9.52

   The Standard Deviation measures how the data are dispersed from the mean. So from this figure I can see that the data values are spread widely from the mean because the standard deviation is high, this means that there is a large dispersion.

   From the calculations I have made for Height I have found out that I am between 6.6% and 9.3% taller than the average Year 11 Pupil. In my hypothesis I predicted I was 10% taller, so I was not far off.

1.Height (Male & Female)

   I will now split the data into male and female because I want to find out if an average Year 11 Male has a 10% bigger height than an average Year 11 Female. I will repeat the calculations and graphs, and compare the two sets of answers I get as I go along. Here are the two tables of grouped data for Male and Female Heights;

Male Data

Female Data

Height (cm)

Frequency

Height (cm)

Frequency

150 ≤ h < 155

0

150 ≤ h < 155

1

155 ≤ h < 160

1

155 ≤ h < 160

4

160 ≤ h < 165

1

160 ≤ h < 165

9

165 ≤ h < 170

4

165 ≤ h < 170

8

170 ≤ h < 175

4

170 ≤ h < 175

2

175 ≤ h < 180

5

175 ≤ h < 180

0

180 ≤ h < 185

6

180 ≤ h < 185

1

185 ≤ h < 190

4

185 ≤ h < 190

0

...read more.

Middle

Height (cm)

Frequency

Cumulative Frequency

150 ≤ h < 155

0

0

155 ≤ h < 160

1

1

160 ≤ h < 165

1

2

165 ≤ h < 170

4

6

170 ≤ h < 175

4

10

175 ≤ h < 180

5

15

180 ≤ h < 185

6

21

185 ≤ h < 190

4

25

image25.png

   Here is my table and graph for Female Cumulative Frequency for Height;

Female Data

Height (cm)

Frequency

Cumulative Frequency

150 ≤ h < 155

1

1

155 ≤ h < 160

4

5

160 ≤ h < 165

9

14

165 ≤ h < 170

8

22

170 ≤ h < 175

2

24

175 ≤ h < 180

0

24

180 ≤ h < 185

1

25

185 ≤ h < 190

0

25

image26.png

   From these graphs for Cumulative frequency I can see that the gradient of the curve for Males is steeper towards the end half of the curve, and the gradient of the curve for Females is steeper at the beginning and then the gradient is very low at the end. This shows that the concentration of smaller pupils is greater for Females, and the concentration for taller pupils is much greater for Male Year 11 pupils. I can also see from the Female Cumulative Frequency graph that there are very few tall female Year 11 pupils, and from the Male Cumulative frequency graph I can see that there are very few small male Year 11 pupils.

5.Median

     Male Median Height = 177.5 cm

     Female Median Height = 164 cm

   From these figures I can see that the Male median Height for a Year 11 pupil is 13.5 cm or 7.6% taller that the median Height for a Year 11 Female, which is not far off my prediction of 10%.

6.Interquartile Range

     Male Interquartile Range

= Q3 – Q1 = 183 cm – 170 cm = 13 cm

     Female Interquartile Range

= Q3 – Q1 = 167.5 cm – 160.5 cm = 7 cm

   Here are my Box and Whisker Diagrams;

image27.png

image28.png

   From the Interquartile Range and the Box and Whisker diagrams I can see that the middle 50% of the Female height data has a much tighter distribution than the middle 50% of the male height data. From the diagrams I can see that the middle 50% of the male data covers the taller heights, and the middle 50% of the female data covers mainly smaller heights.

7.Standard Deviation

     Male Standard Deviation = 8.255

     Female Standard Deviation = 6.018

   From these calculations I can see that the spread of the data from the mean for Females is much tighter than the spread of the data from the mean for Males.

   From these calculations I have found out that an average Year 11 Male is between 7.1% and 11.1% taller than an average Year 11 Female. I will now move on to Weight.

2.Weight (All data)

   I will now do all my calculations and graphs for Weight. I will firstly do them for all the data, I will then split it into male and female and repeat the calculations and graphs. Here is my table of grouped data for the weight of Year 11 pupils, including all my data;

Weight (Kg)

Frequency

40 ≤ w < 45

2

45 ≤ w < 50

3

50 ≤ w < 55

6

55 ≤ w < 60

10

60 ≤ w < 65

9

65 ≤ w < 70

8

70 ≤ w < 75

5

75 ≤ w < 80

4

80 ≤ w < 85

0

85 ≤ w < 90

0

90 ≤ w < 95

2

95 ≤ w < 100

1

1.Histogram

image29.png

   From this Histogram I can see that it has a negative skew, there are three outliers that can be seen on the histogram between 90 and 100. Also, the weights of Year 11 pupils have a tight distribution without the outliers.

2.Mean

     Mean = Sum of Weight =        3129.5 = 62.59 Kg

                 No. of Pupils           50

   Compared to my weight of 68 Kg, the mean weight of a Year 11 pupil is 5.41cm smaller than my weight. As a percentage this is 8.0%, which makes my prediction of 10% almost correct.

3.Mode (Modal Group)

     Mode (Modal Group) = 55Kg ≤ w < 60Kg

   The modal weight for an average Year 11 pupil is 55Kg ≤ w < 60Kg which is 13Kg ≤ w < 8Kg smaller than my weight of 68%. This means my weight is 19.1% ≤ w < 11.8% above average.

4.Cumulative Frequency Graph

   Here is my table and graph for the Cumulative frequency for weight;

Weight (Kg)

Frequency

Cumulative Frequency

40 ≤ w < 45

2

2

45 ≤ w < 50

3

5

50 ≤ w < 55

6

11

55 ≤ w < 60

10

21

60 ≤ w < 65

9

30

65 ≤ w < 70

8

38

70 ≤ w < 75

5

43

75 ≤ w < 80

4

47

80 ≤ w < 85

0

47

85 ≤ w < 90

0

47

90 ≤ w < 95

2

49

95 ≤ w < 100

1

50

image02.png

   From this graph I can see that the gradient of the curve is steep up to 80Kg, and then it hardly goes up at all. The flat line in the curve shows that no pupils from my data have a height of between 80Kg and 90Kg.

5.Median

     Median = 62 Kg

   The median weight of a Year 11 pupil is 6 Kg or 8.8% smaller than my weight of 68 Kg.

6.Interquartile Range

     Interquartile Range   =   Q3 – Q1   =   69.5Kg – 56Kg   =   13.5Kg

image03.png

   From the Box and Whisker diagram and the Interquartile range I can see that the middle 50% of the data covers 25% of the total data, which shows that the data in the middle 50% is tightly distributed.

7.Standard Deviation

     Standard Deviation = 11.671

   From this figure I can see that the data has a high dispersion, and is spread quite far from the mean.

   From all the calculations and graphs I have made for weight I have found out that I am between 8.0% and 19.1% heavier than the average Year 11 Pupil. In my hypothesis I predicted I would be 10% heavier, so my prediction was correct.

2.Weight (Male & Female)

   I will now split the data into male and female because I want to find out if an average Year 11 Male is 10% heavier than an average Year 11 Female, I will do my calculations and graphs for both and compare the figures and results I get as I go along. Here are the two tables of grouped data for Male and Female Weights;

Male Data

Female Data

Weight (Kg)

Frequency

Weight (Kg)

Frequency

40 ≤ w < 45

0

40 ≤ w < 45

2

45 ≤ w < 50

2

45 ≤ w < 50

1

50 ≤ w < 55

1

50 ≤ w < 55

5

55 ≤ w < 60

5

55 ≤ w < 60

5

60 ≤ w < 65

4

60 ≤ w < 65

5

65 ≤ w < 70

4

65 ≤ w < 70

4

70 ≤ w < 75

2

70 ≤ w < 75

3

75 ≤ w < 80

4

75 ≤ w < 80

0

80 ≤ w < 85

0

80 ≤ w < 85

0

85 ≤ w < 90

0

85 ≤ w < 90

0

90 ≤ w < 95

2

90 ≤ w < 95

0

95 ≤ w < 100

1

95 ≤ w < 100

0

1.Histogram

image04.png

image05.png

   From these two Histograms I can see that the data for females seems to show a tighter distribution than the data for males. I can also see from these graphs that the outliers with a high weight all seem to be males. Overall, the gender with mainly small weights seems to be females, and the Year 11 males seem to have heavier weights.

2.Mean

     Mean Male Weight = Sum of Weight = 1669.5 = 66.76 Kg

                                          No. of Pupils        25

     Mean Female Weight = Sum of Weight = 1460 = 58.4 Kg

                                             No. of Pupils        25

   From these results I can see that the mean weight for a Year 11 male is 8.36 Kg more than the mean weight for a Year 11 Female, which is 12.52% heavier on average.

3.Mode (Modal Group)

     Male Modal Weight = 55 ≤ w < 60 Kg

     Female Modal Weight = 50 ≤ w < 65 Kg

   From these figures I can see that the mode for females covers a larger range of weight than the mode weight for males, this is because the frequency for females is the same for three columns in my Histogram.

4.Cumulative Frequency Graph

   Here is the table and graph for Male Cumulative Frequency for Weight;

Male Data

Weight (Kg)

Frequency

Cumulative Frequency

40 ≤ w < 45

0

0

45 ≤ w < 50

2

2

50 ≤ w < 55

1

3

55 ≤ w < 60

5

8

60 ≤ w < 65

4

12

65 ≤ w < 70

4

16

70 ≤ w < 75

2

18

75 ≤ w < 80

4

22

80 ≤ w < 85

0

22

85 ≤ w < 90

0

22

90 ≤ w < 95

2

24

95 ≤ w < 100

1

25

image06.png

  Here is the table and graph for Female Cumulative Frequency for Weight;

Female Data

Weight (Kg)

Frequency

Cumulative Frequency

40 ≤ w < 45

2

2

45 ≤ w < 50

1

3

50 ≤ w < 55

5

8

55 ≤ w < 60

5

13

60 ≤ w < 65

5

18

65 ≤ w < 70

4

22

70 ≤ w < 75

3

25

75 ≤ w < 80

0

25

80 ≤ w < 85

0

25

85 ≤ w < 90

0

25

90 ≤ w < 95

0

25

95 ≤ w < 100

0

25

...read more.

Conclusion

   If I was to do this coursework again I would take all of the measurements myself and measure them in the same way to make it fair. I would also take a larger set of data which would hopefully give more accurate results.

...read more.

This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

  1. Marked by a teacher

    Height and Weight of Pupils

    100 1.60 48 I will investigate these following hypotheses using my sample of data: Hypotheses * Year 8 females will be taller and heavier than year 8 males. * Year 11 males will be taller and heavier than year 11 females.

  2. GCSE Physics Coursework

    So if the weight of the load decreases so does the amount of deflection. This is because the deflection is affected by both the distance from the pivot and the weight of the load. This can be defined by moments which are the rotation caused by a force acting at a distance from the pivot.

  1. Statistics coursework Edexcell

    The gradient of the line of best fit is: Y = mx+c X= 1.785 50/1.4= 35 r 1 50 = 35 x 1.4 + 1 Y= 35X+1 I will now look at BMI to gain an idea of how boy's BMI from each year group differs and of how girl's

  2. Show that different people have different reaction times according to their gender and the ...

    I will make sure each person holds their fore finger and thumb the same distance apart (2cm). In addition I must make sure that each person has no idea when I am about to drop the ruler, otherwise they will know when to close their hand.

  1. Conduct an investigation comparing height and weight from pupils in Mayfield School.

    I will instead be comparing year 7 boys to year 11 boys and the year 7 girls to the year 11 girls. I am hypothesising that the boys and girls in year 7 will have smaller standard deviations than the boys and girls in year 11 for height and weight.

  2. Statistics GCSE Coursework. Height and weight of pupils. The sampling method I am ...

    girls are around the same weight however the boys have a larger spread of data, they both have the same inter-quartile range, however the extremes of the data are larger for the boys. This data could support the hypothesis as it is proven that girls have growth spurts easier than girls.

  1. I am going to find out the year 10 male average student at Weavers ...

    This hypothesis is only for 2009 data. Weight and Height = Continuous data Scatter diagram and Spearman's rank to show the correlation of height and weight, they both techniques also complement each other. To find the equation of the line of best fit from the scatter diagram and look at

  2. Testing 3 Hypotheses on Pupils Height and Weight.

    You can see that the height of KS3 boys and KS4 girls and boys all have a good shape. The bars all fit with the normal distribution curve. The bars are corresponding to my normal distribution curve. As you can see from the graphs it shows that boys are usually taller and weigh more.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work