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• Level: GCSE
• Subject: Maths
• Word count: 4126

# Maths Statistics Coursework

Extracts from this document...

Introduction

Pre-test

I will use the ran method on the calculator and randomly choose 20 random numbers. By using a calculator I am eliminating bias because if you were to choose the numbers yourself you would probably end up choosing numbers that are easier to work with. By taking out bias I will make this investigation fairer. After choosing the 20 number I have deleted all the unwanted columns and just left the height and weight columns.

1.67

66

1.36

45

1.60

53

1.67

52

1.62

48

1.72

58

4.65

53

1.55

50

1.56

60

1.52

45

1.36

45

1.49

37

1.72

56

1.67

66

1.80

49

1.67

66

1.55

36

1.70

49

 1.86

56

 1.55

36

I will now put the data into a scatter graph to see if the correlation is positive.

The linear line shows that the correlation i positive. I know this because it is because it facing upwards witch means the coreelation is positive. There is one anomly in this graph an anomly is a freak result. A positive corraltion shows that as the weight increases so does the height.This gives me proof that my hypothesis has a good chance of being right. I will know using the corral  method worked out the coreleation between heigh and weigh from the 20 pieces of data. The corral method is way of working out corraltion quickly and easly in  microsoft excel. The way you do it is by highlighting the data you wish to use in excell then typing in this fromula in the formula box =Corel (A1:A21, B1:B21. The correlation I got was 0.65214. 65214 is strong positive correlation. The positive correlation I got from the scatter graph and positive correlation has give given me enough reason to investigate hypotheses  “the taller you are the heavier you are” in more depth.

To make my results more accurate I will do a stratified sample of a 150 students.

Middle

1.52

45

Female

9

1.62

52

Female

9

1.8

60

Female

9

1.55

36

Female

9

1.53

65

Female

9

1.6

48

Female

9

1.57

40

Female

9

1.49

37

Female

9

1.62

49

Female

9

1.64

55

Female

9

1.58

40

Female

9

1.6

41

Female

9

1.48

47

Female

9

1.63

52

Female

9

1.65

49

Female

9

1.57

38

Female

9

1.60

60

Male

9

1.56

60

Male

9

1.66

54

Male

9

1.66

70

Male

9

1.52

52

Male

9

1.75

75

Male

9

1.65

45

Male

9

1.52

54

Male

9

1.67

54

Male

9

1.71

60

Male

9

1.80

48

Male

9

1.73

66

Male

9

1.55

50

Male

9

1.77

66

Male

9

1.73

52

Male

9

1.54

44

Male

9

1.47

42

Male

10

1.52

45

Female

10

1.80

60

Female

10

1.67

66

Female

10

1.60

56

Female

10

1.40

45

Female

10

1.73

51

Female

10

1.72

56

Female

10

1.62

48

Female

10

1.75

57

Female

10

1.73

51

Female

10

1.62

48

Female

10

4.65

53

Female

10

1.70

48

Female

10

1.63

60

Male

10

1.75

45

Male

10

1.80

49

Male

10

1.66

70

Male

10

1.90

70

Male

10

1.70

57

Male

10

1.66

66

Male

10

1.60

9

Male

10

1.80

60

Male

10

1.75

56

Male

10

1.55

64

Male

10

1.63

50

Male

10

1.72

58

Male

10

1.54

57

Male

10

1.52

45

Female

10

1.80

60

Female

10

1.67

66

Female

10

1.60

56

Female

10

1.40

45

Female

10

1.73

51

Female

10

1.72

56

Female

10

1.62

48

Female

10

1.75

57

Female

10

1.73

51

Female

10

1.62

48

Female

10

4.65

53

Female

11

1.67

66

Male

11

1.71

57

Male

11

1.52

60

Male

11

1.72

63

Male

11

1.91

82

Male

11

1.77

57

Male

11

1.8

60

Male

11

1.86

56

Male

11

1.81

72

Male

11

1.75

60

Male

11

1.85

73

Male

11

1.72

58

Male

I will now do my pre test to see if my hypothesis is good enough to investigate further. I will know if the hypothesis is good enough to warrant further investigation by working out the correlation between height and weight. And making a scatter graph and seeing if the correlation on it is positive. If the correlations are strong and positive I will have enough proof that the hypothesis is correct if this happens I will investigate the hypothesis further.  The data I am using is continuous this will make the results more varied. The more varied the results are the more options I have in how I will study the data. The continuous data will give me more accurate results and will note cause problems by overlapping like discrete data does.

To do my pre-test I need to have a smaller amount of data than the 150 pieces of data I have got. To be precise I need 25 pieces of data. I will pick 25 pieces of data from the 150 I will do this by using the ran method on my calculator. The ran method is bias free way of choosing data. I am using the ran method because if I was to choose the data myself I would sub-consciously choose the numbers that are easier to work with. So by using the ran method I am making my investigation more fair. And the fairer my investigation is the more credence I can give to my results.

The 25 pieces of data I have picked using the ran method are

 Height (m) Weight (kg) 1.59 45 1.52 52 1.36 45 1.60 53 1.52 45 1.62 48 1.72 58 4.65 53 1.55 50 1.56 60 1.52 45 1.36 45 1.49 37 1.72 56 1.67 66 1.80 49 1.80 60 1.55 36 1.70 49 1.61 47 1.65 56 1.67 66 1.73 66 1.75 57 1.67 53

Conclusion

100 ≤ IQ< 105 because it has the most people fir into it. Most of the year 7 boys have an IQ between 110 and 105. My total frequency which is the same as cumulative frequency is 9. This is correct because I’m worked out I need 7 people in my stratifying sampling.

I will now do a grouped frequency table for boys.

 C Tally Frequency(f) Mid Point (x) End Point Class interval fx 95 < IQ< 100 II 2 97.5 100 5 195 100 < IQ< 105 IIIIIIIIII 9 102.5 105 5 922.5 105 < IQ< 110 I 1 107.5 110 5 107.5 110< IQ< 115 I 1 112.5 115 5 112.5 115 < IQ < 120 0 117.5 120 5 0 120< IQ< 125 0 122.5 125 5 0

Total frequency =12

The table above is the grouped frequency table for boys. The table shows my class intervals, which are of equal widths and my cumulative frequency with mid and end. By looking at this table I can see that the modal group is the 100 to 105 group because it has the highest frequency. My total frequency is 12 I know this is correct because it matches my stratified sampling of year 7 girls.

Comparing the two tables I see that both of the tables have the same model groups. Witch tells me that the average for both is around the same.

I have worked out that the boys average is 102.3333And the girls average is 100.8 this tells me that boys on average have a higher IQ in year 7.Also the boys in is 97 and the girls in 96. The boys max is 112 and the girls max is 107. This tells me that the boys have the highest iq among them and the girls have the lowest.

This disproves my hypothesis that girls have a higher IQ than boys in year 7.

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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