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  • Level: GCSE
  • Subject: Maths
  • Word count: 3197

The relationship between height and weight for students of Mayfield High School.

Extracts from this document...

Introduction

Maths Coursework

Handling Data for Mayfield High School

The Task

The following data is provided.

Year Group

Number Of Boys

Number Of Girls

Total

7

151

131

282

8

145

125

270

9

118

143

261

10

106

94

200

11

84

86

170

Given the above data it is my task to develop a statistical investigation based upon different lines of enquiries.

The lines of enquiries which I may choose to investigate are as follows:

  • The relationship between height and weight
  • The relationship between IQ and key stage 2 results.

I have decided to investigate on height and weight.

Collecting the data

We first need to begin by taking a random sample of data.  I collected a random sample of data for 30 boys and 30 girls as shown below in the table.

BOYS

GIRLS

HEIGHT / m

WEIGHT/ kg

HEIGHT/ m

WEIGHT/ kg

1

1.67

66

1.83

60

2

1.72

63

1.63

44

3

1.80

60

1.73

50

4

1.32

54

1.69

51

5

1.62

56

1.61

54

6

1.69

50

1.70

50

7

1.68

50

1.75

60

8

1.80

72

1.68

48

9

1.85

73

1.58

54

10

1.75

68

1.74

39

11

1.67

60

160

48

12

1.86

80

1.61

45

13

1.62

92

1.63

38

14

1.70

62

1.70

60

15

1.52

38

1.62

54

16

1.72

64

1.56

38

17

1.61

42

1.65

54

18

1.73

50

1.69

46

19

1.70

72

1.52

48

20

1.80

62

1.54

65

21

1.71

57

1.67

52

22

1.85

73

1.73

64

23

1.67

50

1.52

38

24

1.61

47

1.57

48

25

1.62

51

1.60

48

26

2.00

86

1.75

56

27

1.50

35

1.60

45

28

1.62

48

1.73

48

29

1.65

50

1.55

50

30

1.84

76

1.76

56

A more useful representation of data

Although I have collected a rather random sample of data, it is not really very useful to me, in the sense it is simply a series of numbers without much meaning.

...read more.

Middle

55 – 64

||||  |

6

65 – 74

|

1

75 – 84

0

85 - 94

0

Graphical Representation

To help analyse the data in a simple way I have produced bar graphs for both height and weight, for both boys and girls, as shown below.

Heights of Boys and Girls

image04.png

image05.png

To compare the two sets of discrete data, we can compare both sets of results on a dual bar graph as shown below.

image08.png

Series 1 = Boys

Series 2 = Girls

Girls mode height is higher than that of boys, this is feel is quite strange, as id expect boys to be higher.  Also we don’t seem to get no girls shorter than 1.50, yet there exists a boy with a shorter height than any girl.  

Weight of Boys and Girls

image09.png

image10.png

To compare the two sets of discrete data we can record them on a dual bar graph, as shown below.

image11.png

Series 1 = boys

Series 2 = girls

From the graph above it seem that boys have a weight that is more spread out.  Girls seem to be consistent, and don’t seem to weigh more that 74 kg.  The boy’s weight is more spread.  The mode of height is more higher for girls than that of boys.  This is expected, as I feel there must be some sort of relation between height and weight, and if we found the girls to have a higher mode for height in the earlier graph, then the mode for weight for girls should also be higher than boys.

Histograms

As both sets of data collected for both height and weight are continuous, we can also record it on a histogram.

Stem and Leaf

As the data is grouped into class intervals, it makes sense to record it in stem and leaf diagrams.  This will make it easier to read the median values, and calculate the other averages.

Boys Height

Stem

Leaf

Frequency

1.30

2

1

1.40

1.50

2,0

2

1.60

1,1,2,2,2,2,5,7,7,7,8,9

12

1.70

0,0,1,2,2,3,5

7

1.80

0,0,0,4,5,56

7

1.90

2.00

0

1

Boys Weight

Stem

Leaf

Frequency

30

5, 8

2

40

2,7,8

3

50

0,0,0,0,0,1,4,6,7

9

60

0,0,2,2,3,4,6,8

8

70

2,2,3,3,6

5

80

0,6

2

90

2,

1

Girls Height

Stem

Leaf

Frequency

1.30

1.40

1.50

2,2,4,5,6,7,8

7

1.60

0,0,01,1,2,3,3,5,7,8,9,9

13

1.70

0,0,3,3,34,5,5,6

9

1.80

3,

1

1.90

2.00

Girls Weight

Stem

Leaf

Frequency

30

8,8,8,9

4

40

4,5,5,6,8,8,8,8,8,8

10

50

0,0,0,1,2,4,4,4,46,6

11

60

0,0,0,4,5

5

70

80

90

Mean, Median, Mode and Range

To help support the simple analysis from the previous section, comparing the mean, median, mode and ranges of the data collected will help give us more evidence.

Height

Mean:  This can be calculated easily from the frequency tables.

Boys:  1.69m

Girls:  1.65m

Mode:  We can read the modes of the height from stem diagram

Boys:  1.62m

Girls:  1.60m

Median:  There are 30 people in each sample, so the median will be half way between the 15th and 16th values.

Boys:  1.69m

Girls:  1,63m

Range:  The range will show us how spread the data is.

Boys:  0.68m

Girls:  0.31m

Weight

Mean:  This can be calculated easily from the frequency tables.

Boys:  60.23kg

Girls:  50.5kg

Mode:  We can read the modes of the height of the bar chart

Boys:  50kg

Girls:  48kg

Median:  There are 30 people in each sample, so the median will be half way between the 15th and 16th values.

Boys:  60kg

Girls:  50kg

Range:  The range will show us how spread the data is.

Boys:  57kg

Girls:  27kg

Table Summary

We can summarise this data found for both height and weight in a simple table format, to help with other statistical investigation still to be carried out.

Height

Mean

Mode

Median

Range

Boys

1.69m

1.60 – 1.70

1.69m

0.68m

Girls

1.65m

1.60 – 1.70

1.63m

0.31m

Weight

Mean

Mode

Median

Range

Boys

60.23kg

50-60

60kg

57kg

Girls

50.5kg

50-60

50kg

27kg

...read more.

Conclusion

Cumulative frequency curves confirm that boys are taller and weigh more than girls.  The median height for boys is higher than the median height for girls.The box and whisker graphs conclude that in general boys are taller than girls.

Although we were able to analyse all the above points, there are still limitations in our findings:

  • We could have had a better sample, and analyse of results of we were to have taken the age of each student as well.
  • Also out predications are based on general trends observed in the data.  In both samples there were still individuals whose results were outside the general trend.

There was more time available it would be an idea to further the investigation by finding h=out how the relationship between height and weight differs when the age of the students is taken into account as well.

We could test a hypothesis that;

“When age is taken into consideration, the correlation between height and weight will be better than when age is not taken in consideration.”

Due to limitations in time I was unable to further the investigation, but based on the hypothesis, and the results gained from the analysis already carried out I would predict that considering the age would produce a more realistic analysis of the relationship between height and weight.  I think we would also lose the exceptional results which fall outside the generaltrend area, as results would now be more consistent and reliable, as there would be a more larger sample used.

...read more.

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