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  • Level: GCSE
  • Subject: Maths
  • Word count: 6171

Statistics GCSE Coursework. Height and weight of pupils. The sampling method I am going to use is stratified sampling. This method is appropriate as the data is split into strata already (year group/gender)

Extracts from this document...

Introduction

Pilot Study

Year Group

Boys

Strata

Girls

Strata

Total

Year 7

151

image00.png=13

131

image01.png=11

282

Year 8

145

image09.png=12

125

image10.png=11

270

Year 9

118

image11.png=10

143

image12.png=12

261

Year 10

106

image13.png=9

94

image14.png=8

200

Year 11

84

image15.png=7

86

image16.png=7

170

Total

1183

A pilot study is used test the viability of research. It is a study done prior to the main test enabling researchers to improve the design of the main study making the outcome of the test more reliable. To select the data I wanted for my pilot study, I had to take a sample of the data, the reason for doing this is to cut down time, as I would have to sift through all of the data to delete anomalies and if you take a sample it should be representative of the population, as the set of data is therefore made smaller the result I obtain should be more reliable/accurate. However there are some blanks in the data and some data provided is clearly inaccurate (i.e. a year 11, male pupil who is 1.69m tall and

Weighs 5kg) this data is physically impossible and will make my results less reliable (if used), and the conclusion I come to will not be valid. To overcome this problem I will select the next reliable result in the datasheet.

        The sampling method I am going to use is stratified sampling. This method is appropriate as the data is split into strata already (year group/gender) I chose this sampling method as it has many benefits; When the data is divided into strata I can make deductions that might not have been present if I took a simple random sample, for my hypothesis I can see if your height or weight is dependent on your gender and draw conclusions from that. Stratified sampling also

...read more.

Middle

43

48

63

-20

400

1.62

43

42

82.5

-39.5

1560.25

1.61

49

56

28

21

441

1.61

49

41

85

-36

1296

1.61

49

54

37

12

144

1.60

53.5

46

69.5

-16

256

1.60

53.5

46

69.5

-16

256

1.60

53.5

60

15

38.5

1482.25

1.60

53.5

54

37

16.5

272.25

1.60

53.5

56

28

25.5

650.25

1.60

53.5

54

37

16.5

272.25

1.59

58

52

44

14

196

1.59

58

45

74.5

-16.5

272.25

1.59

58

68

6

52

2704

1.58

60.5

45

74.5

-14

196

1.58

60.5

60

15

45.5

2070.25

1.57

62.5

38

93.5

-31

961

1.57

62.5

49

57.5

5

25

1.56

66

74

2

64

4096

1.56

66

47

67

-1

1

1.56

66

59

20

46

2116

1.56

66

50

53

13

169

1.56

66

40

88.5

-22.5

506.25

1.55

70.5

60

15

55.5

3080.25

1.55

70.5

57

24.5

46

2116

1.55

70.5

50

53

17.5

306.25

1.55

70.5

64

10

60.5

3660.25

1.54

75.5

40

88.5

-13

169

1.54

75.5

40

88.5

-13

169

1.54

75.5

43

80

-4.5

20.25

1.54

75.5

48

63

12.5

156.25

1.54

75.5

42

82.5

-7

49

1.54

75.5

54

37

38.5

1482.25

1.53

79.5

40

88.5

-9

81

1.53

79.5

35

97.5

-18

324

1.52

81.5

45

74.5

7

49

1.52

81.5

45

74.5

7

49

1.51

85

38

93.5

-8.5

72.25

1.51

85

45

74.5

10.5

110.25

1.51

85

59

20

65

4225

1.51

85

48

63

22

484

1.51

85

40

88.5

-3.5

12.25

1.50

89.5

52

44

45.5

2070.25

1.50

89.5

49

57.5

32

1024

1.50

89.5

39

92

-2.5

6.25

1.50

89.5

35

97.5

-8

64

1.45

92

72

3.5

88.5

7832.25

1.44

93.5

49

57.5

36

1296

1.44

93.5

49

57.5

36

1296

1.42

95.5

34

100

-4.5

20.25

1.42

95.5

52

44

51.5

2652.25

1.39

97

42

82.5

14.5

210.25

1.36

98

44

78.5

19.5

380.25

1.32

99

48

63

36

1296

1.25

100

35

97.5

2.5

6.25

96476.5

I inputted the results I got from the above table into the equation to get:

image05.png

The answer I got is 0.4 (to 1dp) this proves there is some positive correlation (when used in conjunction with the table on page 4) so I do have some grounds for further investigation. The answer also proves I have a positive linear correlation between the two variables. Based on the value of r2 (0.42108310812 =0.177310984) therefore I can say that with a 17% chance that from any point on the line of best fit an increase in height will lead to an increase in weight. This positive correlation along with the positive correlation shown on the scatter graph, proves that from my pilot study there are grounds for further investigation.

The main study

After the results of my pilot study, I have proven there are grounds for further investigation and produced three hypotheses for this further investigation:

        Hypothesis 1 – As height increases weight increases. This relationship will become stronger as you become older.

        Hypothesis 2 – Boys are taller and heavier than girls.  The difference between boys and girls will increase as the students get older.

        Hypothesis 3 – Height and weight is normally distributed. Around 68% of the data will lie within ± 1 standard deviation from the mean.

        To test these hypotheses I first need to take a sample, I have chosen to sample 6 of the 10 strata, allowing me to make comparisons between the year group and gender the groups are as seen below:

Year 7 Females

Year 7 Males

Year 9 Females

Year 9 Males

Year 11 Females

Year 11 Males

        I have chosen to

...read more.

Conclusion

         Again taking out the outliers for weight did not dramatically alter the result I obtained as I conclusively proved that males were heavier than females earlier in my study. Again as weight is affected by environmental factors over inherited factors extremes can be expected due to obesity/ anorexia both conditions you would expect to find within a school environment. A more in-depth study of their lifestyles, ethnic roots and general health would be needed to make very firm conclusions however with or without outliers I was able to statistically prove my hypothesis.

Conclusion

        Although all of my hypotheses were proven statistically, they were not firmly proven this could be due to the sample size, or the second hand data I have used. I would need to compare the results from this school to other schools to make sure it is representative of all schools in the UK. This first hand data would have to be collected and compared. However time is a limiting factor in my study so the conclusions I have made must be taken into consideration. Again had time not been a limiting factor I could have studied year  8 and 10 to get a better picture of what is happening throughout the students school life and what factors could have contributed to increase in height/weight.

        It has been a useful investigation to provide me with great insight into statistical analysis and improved my analytical skills.

...read more.

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