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  • Level: GCSE
  • Subject: Maths
  • Word count: 3377

GCSE maths statistics coursework

Extracts from this document...

Introduction

GCSE maths statistics coursework

For my maths statistics coursework I am going to be comparing the height and weight of the pupils at Mayfield High School. I will compare height and weight because it is continuous data. Firstly I will take a sample of 5% of the 1183 pupils which will be 59 samples. I think that the taller the person the heavier he or she is.

      I will take the sample by pressing the random button on the calculator and taking the sample which is equivalent to that number. The table below shows the samples that I got.

no.

height

weight

6

1.77

54

832

1.66

66

48

1.65

45

813

1.75

56

852

1.55

64

783

1.61

52

131

1.50

70

911

1.70

50

252

1.58

65

354

1.55

64

504

1.48

40

538

1.58

48

2

1.57

53

272

1.75

55

344

1.45

51

894

1.62

52

1046

1.71

54

990

1.74

50

48

1.65

45

314

1.64

42

531

1.43

41

1131

1.61

59

333

1.78

50

718

1.59

64

445

1.72

53

853

1.75

57

654

1.58

58

113

1.63

47

27

1.56

53

1162

1.76

56

503

1.70

52

610

1.74

70

881

1.32

45

801

1.52

33

43

1.52

37

711

1.72

42

1061

1.68

58

32

1.52

52

377

1.70

42

642

1.71

68

391

1.59

44

317

1.60

41

112

1.62

40

934

1.79

72

198

1.62

54

656

1.61

35

929

1.63

54

262

1.75

60

737

1.60

74

636

1.53

47

923

1.68

50

939

1.80

72

122

1.80

62

334

1.53

40

545

1.64

47

656

1.61

35

865

1.63

48

534

1.71

40

143

1.62

48

1007

1.66

63

I will start by plotting a scatter graph of the height of the pupils against their weight.

image00.png

The graph shows that there is positive correlation. It tells us that as the taller the pupil the heavier he or she is but there are a few exceptions. The line of best fit tells us that a person who is 1.6 meters weighs about 51 kilograms. I can also work out how strong the correlation is, 0 being the weakest correlation and 1 being the strongest correlation. The co efficient is 0.320191 which tells us that there is a weak positive correlation.

      I have found

...read more.

Middle

31

1.67

52

994

1.68

50

392

1.59

68

811

1.42

30

931

1.62

51

401

1.59

47

I will now draw a scatter graph of height and weight for the girls and for the boys.  

image01.png

     The graph shows that there is a positive correlation. The graph shows that the taller the girl the more she weighs but there are a few exceptions. I will now work out the how good the correlation is. I worked out that the correlation co-efficient was 0.431499. This tells us that the correlation is positive but it is not to strong.

     I will now draw a scatter graph for the boys and compare the strength of the correlation with that of the girls to see if it is better or worse.

image04.png

The graph also shows that as the height of the boys increases their weight also increases with a few exceptions. I can now work out how good the correlation is and compare it to the strength of the correlation form the graph of the girls.

     The strength of the correlation was 0.524631 which is higher than the 0.419718 for the girls but it is not much higher. This tells us that  ???????????????????????

I will now draw a histogram of the height of the boys and girls and compare them to see which of the two genders is taller and how the range of their heights. I predict that the boys will generally be taller than the girls and that the range of heights will be larger for boys than that of the girls. The table below is a summary of the boys data.

Height

frequency

class width

Frequency density

1.3<x<1.4

1

0.2

5

1.4<x<1.5

2

0.2

10

1.5<x<1.6

10

0.2

50

1.6<x<1.7

12

0.2

60

1.7<x<1.8

3

0.2

15

1.8<x<1.9

2

0.2

10

        The first 2 rows and the last 2 rows had a low frequency so I grouped them together to give a higher frequency which would show a better representation of the data.

height

frequency

Class width

Frequency density

1.3<x<1.5

3

0.3

10

1.5<x<1.6

10

0.2

50

1.6<x<1.7

12

0.2

60

1.7<x<1.9

5

0.3

16.6

The histogram is plotted on the next page.

The histogram shows that most of the boy’s height is in the range of 1.5m to 1.7m but there are a few exceptions on either side of this range. Most boys are in the height range of 1.6m to 1.7m and the frequency density being 60.

    I will now draw a histogram of the girl’s heights. The table below shows the summary of the girl’s data.

height

frequency

class width

freq. density

1.4<x<1.5

8

0.2

40

1.5<x<1.6

12

0.2

60

1.6<x<1.7

4

0.2

20

1.7<x<1.8

3

0.2

15

1.8<x<1.9

2

0.2

10

The histogram is drawn on the next page.

The histogram shows that the majority of girls were in the height of 1.5m to 1.6m. There were also a high frequency of girls who were in the height range of 1.4m to 1.5m and there was only a low frequency of girls between 1.6m to 1.9m.

     The histograms show that the boys are generally taller than the girls with the majority of boys being in the height range of 1.6m to 1.7m compared to the majority of the girls height range which is between 1.5m to 1.6m. This shows that my prediction that the boys were generally taller than the girls was correct but I was not correct in predicting that the range of heights was larger for boys than that of the girls as both went up to 1.9m although the frequency density between 1.7m to 1.9m was larger than the frequency density of the girls.

     I will now do frequency polygons of the girls and boys weights. I will use the same samples I used for the histograms. The frequency polygons will help me compare the two visually. I predict that the girls will weigh more than the boys but the boy’s weight will be more spread out than the girls. I predict that the girls will weigh more than the boys because as the go through puberty they gain fat in places where boys don’t so they will tend to weigh more.  The table below shows the data that I will be plotting in the frequency polygon for the weight of the girls.

weight

30-39

40-49

50-59

60-70

frequency

3

12

8

6

image05.png

The frequency polygon shows that most girls weigh between 40 to 49 kg but there are quite a few girls that weigh between 50kg and 70kg. The frequency polygon also shows that there are only a few amount of girls that weigh between 30kg and 39kg.

     I will now draw a frequency polygon of the boy’s weights. The table shows the data that I will use.

weight

30-39

40-49

50-59

60-69

70-79

frequency

3

10

10

5

2

image06.png

The frequency polygon shows that most of the boys weigh between 40kg and 59kg. It also shows that there exceptions either side of the weights. The frequency polygon also shows us that the boys have a very wide range of weights starting at very skinny people to people who weigh a lot.  

I will now plot the weight of the boys and girls on the same frequency polygon and compare the results.

image07.png

The results show that the majority of girls weigh between 40kg and 49 kg and there are quite a few girls that weigh between 50kg and 59kg. The majority of the boy’s weight is more spread out than the girls. The frequency for the majority is only 10 compared to the girls 12 but is spread out over a larger area of weight. The boys also tend to weigh more than girl. This is shown in the graph where the girl’s weight only goes up to 66kg and the boy’s weight goes up to 72kg. Overall the graph shows that the girls weigh more but the range of weight is wider for the boys than for the girls.

I will now have a look at the different year groups and see if it shows the same relationship as the relationship between the general amount of boys and girls. I will draw cumulative frequency graphs of the height of the boys first and compare them using box and whisker plots. I will then do the same with the girls and compare them using box plots. Finally I will compare the boys with the girls. I will start by taking a stratified sample of the different year groups.  I will be taking a sample of 10% of boys and girls from years 7 to 9.

Sample of girls from year 7-

71

1.63

45

545

1.64

47

742

1.73

49

109

1.59

54

259

1.56

57

243

1.25

35

515

1.75

40

542

1.43

38

29

1.52

40

460

1.57

45

695

1.80

110

801

1.52

33

596

1.52

52

Samples of boys from year 7 –

593

1.55

45

762

1.51

39

802

1.53

45

805

1.60

38

173

1.59

52

481

1.54

51.5

464

1.50

40

501

1.47

47

665

1.54

40

746

1.53

40

792

1.55

32

54

1.52

25

328

1.51

45

597

1.62

47

752

1.62

47

Sample of girls from year 8 –

74

1.45

49

237

1.55

60

283

1.60

42

408

1.59

44

566

1.57

51

16

1.55

42

557

1.43

49

718

1.59

64

719

1.72

57

789

1.56

45

322

1.69

61

654

1.58

58

130

1.35

51

...read more.

Conclusion

The box plots show that the range of heights for girls is a lot larger than the range of heights for boys.  This shows us that in year 7 the tallest girl is a lot taller than the tallest boy but the shortest girl is a lot shorter than the shortest boy. The interquartile range is larger for the girls than for the boys and the median is also larger for the girls which shows that the average height of the girls in year 7 is bigger than the average height of the boys.

I will now compare the height of the boys and girls from year 8.

The box plots show that the boys have a wider range of heights. The boys also have a wider interquartile range but the average height is taller for the girls. The average height for girls in year 8 is higher than the average height of girls in year 7 but is less for the boys.

I will now compare the height of the boys and girls from year 9.

The box plots show that the range of heights for the boys is higher up the scale than that of the girls which shows that girls have the shortest height and the boys have are the tallest. The average height for boys is 1.7m which is a lot bigger than the average height of the girls which is 1.61m therefore the boys are generally taller.

...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.

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