Stratified sampling and Hypotheses - Taller people tend to be heavier - Males are taller than females - Males height is more variable than females

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INTRODUCTION 2

Stratified Sampling Method 2

Sample 5

PLAN 8

HYPOTHESIS 1 9

Scatter graphs 9

HYPOTHESIS 2 11

Mean 12

Median 13

Grouped Frequency Tables 13

Histograms 14

Cumulative Frequency 16

Stem and Leaf Diagram 17

Relative Frequency 18

HYPOTHESIS 3 19

Range 19

Sample Standard Deviation 19

CONCLUSION 22

INTRODUCTION

For this investigation, I was given a collection of data with 328 records. These records were of students with certain details about themselves. These details included:

- Mathematics Set

- Height (cm)

- Weight (kg)

- Shoe size

- Hand span size

I realized that this database containing 328 records of students was too large to work with. Therefore I decided to create a sample of this database using the stratified sampling method.

Stratified Sampling Method

Firstly, I counted the total number of male and female students in each math's set. I used a tally chart to help me with this:

Math's Set

Male

Female

Red

Mauve

Blue

Green

I then counted each tally to receive the following numbers:

Red:

58 male, 65 female

Mauve:

31 male, 40 female

Blue:

53 male, 63 female

Green:

2 male, 5 female

Once I finished counting the number male and female students from each math's set, I added up all my results:

56

65

32

40

53

63

12

+ 5

328

The reason I added all my results together is because if all the results added together did not equal 328, I would have not counted properly and missed students out because the total number of students is 328. I then calculated the percentage of the male and female students of each category out of the total 328 students:

Percentage of Red Males

56

328

To the nearest whole number = 17%

Percentage of Red Females

65

328

To the nearest whole number = 20%

Percentage of Mauve Males

32

328

To the nearest whole number = 10%

Percentage of Mauve Females

40

328

To the nearest whole number = 12%

Percentage of Blue Males

53

328

To the nearest whole number = 16%

Percentage of Blue Females

63

328

To the nearest whole number = 20%

Percentage of Green Males

12

328

To the nearest whole number = 4%

Percentage of Green Females

5

328

To the nearest whole number = 2%

Now that I have calculated the percentages for the number of students in each math's set, I can use these percentages to choose my sample. I will use the figure that I obtained from each percentage calculation to choose the number of male and female students for each category. Otherwise known as each strata which basically means layer, in this case our chosen strata are the different categories of math's set e.g. red, blue, mauve etc. For example, the percentage I received for the males in the red math's set was 17%. Therefore at random, I will pick 17 males of the red math's set and include them in my sample from the database of 328 students. I will use the same approach to select the rest of the students for my sample. Therefore in total I will have 17 males from the red math's set, 20 females from the red math's set, 10 males from the mauve math's set, 12 females from the mauve math's set, 16 males from the blue math's set, 19 females from the blue math's set, 4 males from the green math's set and 2 females from the green math's set. The reason why I used the percentages that I calculated as guidance to the amount of students I should extract from each category out of the entire database is because, percentages are out of a 100. Therefore with this approach, with all my chosen students added together, I will have 100 different students which will make up my complete sample.

I chose the stratified sampling method because it was most appropriate to use seeing as the database has several different strata. By using this method, the proportion of each strata in the sample will be more accurately matched to the proportion of each strata from the database. This would provide me with a more accurate sample to represent the entire database:

Sample

No.

Math's Set

Male/Female

Height (cm)

Weight (kg)

Shoe Size

Hand Span 1d.p

035

Red

M

70

69

0

25

037

Red

M

69

69

7

22

049

Red

M

80

65

0.5

23

030

Red

M

70

60

9

21.5

031

Red

M

79

73

0

22.5

032

Red

M

72

70

8

23

034

Red

M

72

59

0.5

20.5

035

Red

M

70

69

0

23

036

Red

M

60

45

5

20

037

Red

M

69

69

7

22

040

Red

M

72

58

9

23.6

043

Red

M

85

90

9.5

24

046

Red

M

77.5

49

1

2.5

047

Red

M

73.75

50

2

23

048

Red

M

74

62

9

20

049

Red

M

80

65

0.5

23

073

Red

M

65

63

0

24

008

Red

F

87

70

6.5

20

024

Red

F

70

46

7

9

025

Red

F

78.5

60

6.5

20.5

026

Red

F

66

46

5

21.6

027

Red

F

63

63

6

22

028

Red

F

77

60

8

22

029

Red

F

60

53

5.5

9

033

Red

F

63

47

6.5

20

038

Red

F

69

58

6

22

039

Red

F

80

70

8

22.3

041

Red

F

63

43

5

20

042

Red

F

60

43

4

8

044

Red

F

67

62

6

9.5

074

Red

F

66

50

5.5

9

075

Red

F

75

61

9

9.5

079

Red

F

58

51.5

4

20

080

Red

F

65

53

5

7.4

081

Red

F

65

54

6

9

082

Red

F

63

63

7

8.6

311

Red

F

67

75

7

8.5

000

Mauve

M

76

62

8

9.9
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001

Mauve

M

74

57

0

21.8

002

Mauve

M

78

55

8.5

8

003

Mauve

M

72

52

9

24

004

Mauve

M

75

60

9

23.5

018

Mauve

M

84

60

1

21

019

Mauve

M

60

56

7

21

050

Mauve

M

75

63

1

21

...

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