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  • Level: GCSE
  • Subject: Maths
  • Word count: 3106

For this investigation I have chosen height and weight and find out if gender affects these statistics.

Extracts from this document...

Introduction

Introduction

For this coursework, I was given data from Mayfield High School to help me with my investigation. I was given a list of lines of enquiry and for this investigation I have chosen height and weight and find out if gender affects these statistics.

Plan

As I have mentioned in my introduction, I'm going to investigate the following lines of enquiry: height in contrast to weight; also I will find out if these vary for one specific gender. Firstly I will collect 30 samples of girls and boys from Year 11 at Mayfield High and compare the lines of enquiries to both genders.

To collect a sample of 30 students, I will use random sampling, for this I will need the help of a calculator; by pressing the "shift" button and then the "Ran#" button, multiply by 100, and press the equal button to get a student's number( between 1 and 100 ). If the same number comes up twice, I will just press the equal button again to give me another number.

Then for the second part of my coursework, I will record the weight and height of the boys' and girls' separately and insert these results on a table, plot them into a graph and from there, I will be able to analyse and compare, I will be able to form a conclusion on whether gender affects height and weight.

After doing all that, I will tally up the results, and use the frequency to find out the mean and mode of my collected data.

...read more.

Middle

3

18

1.75

6

24

1.80

5

29

1.85

1

30

Cumulative Frequency table for Weight.

Weight (< or =)

Frequency

Cumulative Frequency

45

2

2

50

6

8

55

8

16

60

10

26

65

3

29

70

0

29

75

0

29

80

1

30

Using my graphs, I was able to find out the upper quartile, median and lower quartile. The results are as below:

To find the Lower Quartile, the following formulae can be used:

1/4      total number of frequency =

1/4      30 = 7.5

To find the Median, the following formulae can be used :

1/2      total number of frequency =

1/2      30 = 15

To find the Upper Quartile, the following formulae can be used :

3 ( 1/4     total number of frequency ) =

3 ( 1/4     30 ) = 22.5

To find the Interquartile range, the following formulae can be used:

Upper Quartile       Lower Quartile =  Interquartile Range

15 - 5 = 10

According to my scatter graph, there is a positive correlation between height and weight. This suggests that the taller the person is, the heavier they will be.

The line of best fit suggests that somebody who's around 1.71m tall, will be around 60 kg .

I will now use the information I gathered from the cumulative frequency curves to draw box and whisker diagrams, showing the minimum and maximum values, the median, and the upper and lower quartiles.

Box-and-Whisker diagram for Height

Box-and-Whisker diagram for Weight

In the next part of my coursework, as I have suggested in my plan, that height and weight are both affected by gender; I will therefore extend my line of enquiry to investigate how the correlation between height and weight is affected by gender. I will now test the hypothesis, that of ; "There will be a better correlation between height and weight if we investigate males and females separately."

I will now collect 30 samples of girls and boys separately, using the same method as before (Random Sampling), and record their height and weight in the table below:

Boys

Girls

Height (m)

Weight (kg)

Height (m)

Weight (kg)

1.60

49

1.65

54

1.72

58

1.69

51

1.85

63

1.55

55

1.80

60

1.47

45

1.65

64

1.61

74

1.80

49

1.73

51

1.52

60

1.65

63

1.72

63

1.62

54

1.91

82

1.83

60

1.55

65

1.65

52

1.54

66

1.68

48

1.75

45

1.70

48

1.72

58

1.71

54

1.86

56

1.55

36

1.70

60

1.62

54

1.78

67

1.72

56

1.63

50

1.67

52

1.81

72

1.62

48

1.71

60

1.83

60

1.77

57

1.60

56

1.62

56

1.72

51

1.60

50

1.67

66

1.55

64

1.76

52

1.65

64

1.61

54

1.75

56

1.70

48

1.55

65

1.62

56

1.77

57

1.40

45

1.66

66

1.72

51

1.75

68

1.62

48

Having done those two graphs, I can now say that the evidence supports the prediction I made earlier: "There will be a better correlation between height and weight if we investigate males and females separately."

The line of best fit on the graphs, show that a girl who is 1.70m tall, would weight approximately 55kg, whereas a boy of the same height would weigh about 60kg.

I will now find the equations of my lines of best fit from the graphs, by finding their gradients and the intercept on the y-axis.

Y will be representing height in metres, and X will be representing weight.

Boys:y  = 60 x + 1.54

Girls:    y  = 55 x + 1.39

Mixed: y  = 61 x + 1.58

These equations could be used to make predictions of weight, if you already know the height, and vice versa. For example, to predict the weight of a girl who is 1.65m tall:

Y = 55 x + 1.39

X =    y - 1.39

         55

If  y = 1.65 then:

X =   1.65 - 1.39  = 1.62

55

Although the line of best fit, is the best estimation of relationship between height and weight, there are exceptional values in my data ( for example: the girl who is 1.61m tall, and weighs 74kg. ) which don't fit in the general trend/pattern.

I will now draw up a cumulative frequency table and graph for height using the 30 samples of girls and boys I have gathered.

Heights (m) < or =

Boys

Girls

           <130

0

0

 <140

0

1

<150

0

1

<160

7

4

<170

6

16

<180

13

6

<190

3

2

<200

1

0

Weights (kg) < or =

  Boys        

Girls

<50

5

9

<55

0

13

<60

12

5

<65

7

1

<70

4

1

<75

1

1

<80

0

0

<85

              1

0

I will now put the data I gathered into two tally charts ( height and weight ) to find the frequency which I will use to get the mean and the mode of the information. I will do this seperately for boys and girls.

The Boys' Tally Chart for Height

Height

Tally

Frequency

1.51 - 1.55

11111

5

1.56 - 1.60

11

2

1.61 - 1.65

1111

4

1.66 - 1.70

11

2

1.71 - 1.75

11111 11

7

1.76 - 1.80

11111 1

6

1.81 - 1.85

11

2

1.86 - 1.90

1

1

1.91 - 1.95

1

1

...read more.

Conclusion

The points on the scatter diagram for the girls are less dispersed  about the line of best fit than those for the boys. This suggests that the correlation is better for girls than boys; and also that girls' heights are less predictable.

The points on the scatter diagram for boys and girls are as much dispersed as for that of the boys' scatter diagram. This suggests that when girls' data is considered separately, the correlation between height and weight is better than when mixed together with the boys.

The scatter diagrams can be used to give reasonable estimates of height and weight. This can be done by either reading from the graph or by using equations of lines of best fit.

My cumulative frequency curves suggest that, in general, boys weigh much more than girls, and they're also taller as well.

The median height and weight for boys are higher than the girls'.

From the box plots ( box and whisker diagrams ), we can say that boys are taller than girls, as well as being heavier. By investigating boys and girls separately, we can get a much narrower conclusion on boys' and girls' heights and weights.

My prediction was based on general trends, in both samples, there were some individuals who fell out of the general trend.

In conclusion, I would say that, it's quite obvious without doing necessary back-up investigation that; boys in general are slightly taller and heavier than most girls, however, as I have mentioned above, there were a few results which fell out of the general trend, although those didn't particularly affect my investigation much.

Bibliography: Edexcel GCSE Mathematics. (Higher)

...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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