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  • Level: GCSE
  • Subject: Maths
  • Word count: 9932

Data from Mayfield high school. It consists of 1183 people, split into 604 boys and 579 girls from the year groups 7-11. The information we've been provided contains a lot of information including: first name, surname, height weight, age, month

Extracts from this document...

Introduction

MAYFIELD HIGH SCHOOL

Introduction

For my investigation I’m going to use data from Mayfield high school. It consists of 1183 people, split into 604 boys and 579 girls from the year groups 7-11. The information we’ve been provided contains a lot of information including: first name, surname, height weight, age, month of birth, KS2 results etc. I have chosen to investigate the relationship between height and weight, as I feel they’ll show a good relationship and may influence each other.

I will investigate the following statements:

  • The relationship between height and weight and see how it varies within gender.
  • Compare the height to weight ratio in terms of body mass index.
  • Compare the height and weight between each of the year groups.

Where the data can be found

The data can be found on the school computers (located on the “W” drive, under MY COMPUTERS)

I’ve chosen there sources of information because…

I have chosen these sources of information, as the data is continuous and therefore there is a wide range of data and therefore I can make more predictions and hypothesis. The data is also quantative and so I can carry out my investigation even further.

The data is reliable because:

This data is reliable, as it has been taken from real people and therefore this data really exists and the values are not made up. (Anomalies are taken into account for, and are simply eliminated)

Prediction/hypothesis

  • I predict that there will be a positive correlation between height and weight in the whole school. I predict that there will be a positive correlation between height and weight in each year group but there will be a poorer positive correlation as age increases. Girls will tend to have a better positive correlation than boys.
  • Average boys’ weight will be larger than the average girls’ weight.
  • People who walk will tend to have a low body mass index that fits their “age frame” (Between 20-25) compared to people who take any other forms of transport. People who travel by bicycle will have a lower body mass index (i.e., they’ll tend to be in the underweight region for BMI)  than people that take any other forms of transport including walking.
  • The spread of boys’ weight will be larger than the spread of girls’ weight.

I should collect data of the height and weight of 60 pupils. I will choose a certain number of pupils from each year group and also choose and equal number of boys and girls from each year group. This means that in my overall data I should have data of 30 boys and 30 girls.

Data

In order to make data sample fair and unbiased I will do a random stratified sample, which means I will have a certain number of boys and girls from each year group in correlation to their percentage of school size.

The data may have some anomalies (for e.g. a year 11 pupil might be less than 1 meter tall or might weigh less than 25 kg) in which case I will simply eliminate that sample and select another one of the same sex and age at random.

I will now carry out an investigation of my hypothesis I made by drawing an assortment of;

  • Graphs (bar, line, cumulative frequency graphs, histograms)
  • Diagrams ( box and whisker etc)
  • Using several calculations
...read more.

Middle

39

0

68

2

40

0

69

0

41

2

70

0

42

1

71

0

43

0

72

1

44

0

73

0

45

3

74

0

46

1

75

0

47

1

76

1

48

1

77

0

49

0

78

0

50

1

79

0

51

0

80

0

52

0

81

0

53

0

82

0

54

0

83

0

55

1

84

0

56

2

85

0

57

1

86

0

58

2

87

0

59

0

88

0

60

0

89

0

61

0

90

0

62

1

91

0

63

3

92

1

Total  = 30

Ungrouped data for boys

Mean: 54.2

Median: 55.5

Mode: 35,45, 63

Girls’ weight

Weight

Frequency

Weight

Frequency

33

1

63

0

34

0

64

0

35

0

65

0

36

0

66

1

37

0

67

0

38

2

68

0

39

0

69

0

40

1

70

0

41

0

71

0

42

2

72

1

43

0

73

0

44

0

74

0

45

4

75

0

46

2

76

0

47

0

77

0

48

4

78

0

49

1

79

0

50

0

80

0

51

1

81

0

52

1

82

0

53

0

83

0

54

0

84

0

55

0

85

0

56

1

86

0

57

1

87

0

58

1

88

0

59

1

89

0

60

1

90

1

61

1

91

0

62

1

92

1

Total = 30

Ungrouped data for girls

Mean: 52.73

Median: 48

Mode: 45, 48

(Ungrouped)

Girls weight

Boys weight

Mean

52.73

54.2

Median

48

55.5

Mode

45,48

35,45, 63

As part of my investigation I have proved my hypothesis right as you can see from the evidence that I have collected above. I calculated the mean and median using a program called autograph as well as calculated it manually to double check that I’ve done everything correctly. As you can see boys have a larger mean than girls, which means that boys are generally heavier than girls thus proving my hypothesis right. Again, boys have a larger median than girls which seems to suggest that boys have a larger average value than girls so proving my hypothesis right in saying boys have a larger average weight than girls. Boys have the highest mode so it seems to suggest that boys are generally heavier than girls, proving my hypothesis right.

I could also just “shoot up” a stem and leaf diagram just to show that boys have more values in the higher regions of weight (i.e. within 50kg and 70kg) than girls whose values tend to be more concentrated around the lower weights (i.e. with 35 and 60 kg)

STEM AND LEAF DIAGRAM

BOYS

GIRLS

:0:

:10:

:20:

8 5 5 5

:30:

3 8 8

8 7 6 5 5 5 2 1 1

:40:

0 2 2 5 5 5 6 6 8 8 8 8 9

9 9 7 6 6 5 0

:50:

1 2 6 7 8 9

8 8 4 3 3 3 2

:60:

0 1 2 6

6 2

:70:

2

:80:

2

:90:

0 2

:100:


As you can see from the comparison of the boys and girls in the stem and leaf diagram above you can immediately spot that the girls weight are mostly found on the “40s” region where as boys weight although found in the same region as well more values are found in the higher regions (60s and 70s) than girls thus showing us that boys have a larger average weight than girls. Though this method is not the most accurate ways of carrying out my hypothesis it is a useful measure and helps us to make a rough estimation.

If data was of the whole school was based around this group of 60 pupils I could predict that a girl chosen at random would have a probability of 0.53 to weight between 30/40 kg and a probability of 0.40 to weight between 50/60kg and a probability of 0.06 to weight in the higher region (i.e. around 90/100 kg).

If I was to pick a random boy I could predict that he’s probability of weighing between 30/40kg would be 0.43 and the probability of him weighing between 50/60kg would be 0.53, 0.13 (or 13%) more than the probability of a random girl having that probability. The boy’s chance of weighing between 90/100kg would be 3% or a probability of 0.03, purely based on statistics. So as you can see a boy has a higher chance of weighing more than a girl.

Grouped data for girls

Grouped weight

Frequency

Midpoint

Midpoint * frequency

Total

30<x40

4

35

4*35

140

40x50

13

45

13*45

585

50<x60

7

55

7*55

385

60<x70

3

65

3*65

195

70<x80

1

75

1*75

75

80<x90

1

85

1*85

85

90<x100

1

95

1*95

95

Total: 30

Total: 1560

Cumulative frequency graph for girls

image16.png

Grouped data for boys

Grouped weight

Frequency

Midpoint

Midpoint * frequency

Total

30<x40

4

35

4*35

140

40x50

10

45

10*45

450

50<x60

6

55

6*55

330

60<x70

7

65

7*65

455

70<x80

2

75

2*75

150

80<x90

0

85

0*85

0

90<x100

1

95

1*95

95

Total: 30

Total: 1620

Cumulative frequency graph for boys

image17.png

Comparing the cumulative frequency of boys and girls

image18.png

Key

                                      Lower quartile markimage02.png

                                     Median markimage03.png

                                     Upper quartile markimage04.png

(Grouped)

Boys

Girls

Mode

40<x50

40<x50

Mean

54.33

53

 Median

52.8571

48.5514

As you can see, I’ve grouped all the data. This has yet again proved my hypothesis right, as shown by the cumulative frequency graph above and the results (mean, median) obtained from it; although the mode for both boys and girls lie on the same range you can see that boys have got a higher value for the mean and median proving that boys have a larger average weight than girls and so proving my hypothesis right. The cumulative frequency graphs basically show me what I have calculated in the table above. I have just included it as a sort of assurance to back up my hypothesis for example if you look at the cumulative frequency graph for girls you can notice that it has a very steep gradient in around the median (50%) so seeming to suggest that most of the girls weights are concentrated between 40-50kg and as you can see from the table above, that was what we calculated as the modal group.

If I was to look at the cumulative frequency graphs I worked (using autograph) that the girls have a lower quartile of 45 while boys have a lower quartile of 44.25. On the other hand boys have a higher median and upper value (median for boys’ ungrouped data=55.5 while girls median=48. Upper quartile for boys=63 while girls’ upper quartile=59.25). All this suggests the boys have less values concentrated in the low regions of the weight scale and as you can see (from the median and upper quartile) boys’ probably have more values, than girls, concentrated in the higher regions of the weight scale meaning that the have a larger average weight than girls, proving my hypothesis right.

image05.png

image20.png

GREEN FILLED HISTOGRAM- BOYS’ HISTOGRAMimage06.png

NON FILLED HISTOGRAM-GIRLS’ HISTOGRAM

I have drawn up a histogram, using ‘Autograph’, for both boys and girls and they are being compared on the same statistics page. Firstly you can notice both histograms have a normal distribution. As you can tell girls and boys have the same modal class (group with most set of values), 40-50. However as you can see that boys have less values than girls in the modal class and this is shown by the shorter  bar, seeming to suggest that most of the boys values for weight are found in the higher regions and this is proved right by looking at the histograms. As you can see as group size increases boys have more values concentrated in those regions than girls, and this is shown by the taller bars. This seems to say that boys have more values in the higher region so seeming to suggest that they have a larger average weight than girls, proving my hypothesis right.

Conclusion

In conclusion I have proved my hypothesis in saying that boys have a larger average weight than girls. I have proved this in both sets of data I have taken, grouped and ungrouped. Although I have proved my hypothesis right there is not much difference in the average boys’ weight with the average girls weight though boys do tend to have a larger average weight. There are several reasons why this is true. Firstly adolescent girls are thought to suffer from a disease known as coeliac disease which is a disease where the body is gluten intolerant so sees them losing a lot of weight or the inability to gain weight. People suffering from this disease may eat a lot but not put on any weight. This could lead to a disease similar to Osteoporosis (osteoporosis is suffered by older women), which is a disorder where the bones become weakened by loss of substance and results in bone mass reducing by 1% every year. This disease (coeliac) is more significant in girls and the disease similar to osteoporosis see’s girls losing their bone mass at a faster rate than girls.

Hormones, such as estrogen and testosterone cause an increase in weight in both girls and boys. The skeleton in girls grows much the same way as in boys however boys end up having a structure where the bones are much heavier and denser thus meaning that boys will tend to be heavier than girls.

Another proposed reason as to why boys have a larger average weight than girls is the fact that girls (and boys to a lesser extent) are affected by the ‘slimmers disease’-anorexia nervosa. Research shows that boys are 4 times less likely to suffer from the disease than girls. Symptoms include; loss of weight, refusal to eat, abnormal fear of being fat and a desire to be thin. All this leads to having a slimmer body and being thinner and less heavy than boys. Also teenage girls are far more likely to diet than boys (even if they are not overweight) and this is due to the growing pressure of looking glamorous which is not that significant in boys. Researchers have shown that students of 15 years old 26% of girls are on diets compared to just 5% of boys. Also by 15, 25% of medium weight and 8% of low weight girls said they were dieting compared with under 3% of medium to low weight boys (according to Dr Helen Sweeting, a researcher at the medical research council social and health sciences unit at the University of Glasgow). Recent reports have also shown that Women pregnant with boys tend to eat about 10 percent more calories a day than those carrying girls but don't gain more weight. The study, published Medical Journal, appears to explain — at least in part — why newborn boys are heavier than girls. This would also if mean that the boy would be more likely to be heavier than the girl when they reach adolescence.

Disregarding all the research, from general knowledge I know that boys will tend to be heavier than girls as boys’ bodies are well built and an Increase in muscle strength occurs after an increase in mass. Boys’ muscles begin to come up between the age of 12-18 and as I mentioned earlier, this only occurs after an increase in mass. Girls tend not to experience this so their physique remains pretty much the same and so their weight does not go up as significantly as boys would.

image21.pngimage22.png

The graphs above are to show roughly how much a girl/boy should weigh between the ages of 1-18. If you were to look and compare the percentiles you can see that at each of them boys will tend to expect to weight more than girls for e.g. at the 75th percentile girls should expect to weigh 68kg while boys are expected to weigh roughly around 79kg. Even at the boys’ 50th percentile it is higher than the girls’ 75th percentile (75kg to girls’ 68kg).

In conclusion my hypothesis in saying that the average boys weight is larger than the average girls weight is proven correct.

HYPOTHESIS 3

My third hypothesis states that people who walk will tend to have a lower body mass index than people who take any other forms of transport. I also stated that people that walk are more likely to fit into their BMI category (i.e. between 20-25).

BMI-Body mass index, or BMI, is a new term to most people. However, it is the measurement of choice for many physicians and researchers studying obesity. BMI uses a mathematical formula that takes into account both a person's height and weight. BMI equals a person's weight in kilograms divided by height in meters squared. (BMI=kg/m2). The chart below shows what the body mass index of people and it tells us of their status.

BMI

Weight Status

Below 19.8

Underweight

19.9 – 24.9

Normal

25.0 – 29.9

Overweight

30.0 and Above

Obese

...read more.

Conclusion

image28.png

However after calculating the skewness for grouped data for boys and girls it sort of contradicts what I concluded from my ungrouped data. I calculated the skewness as 0.5733 for girls while boys’ have s skewness of -0.40896, meaning that the values for girls are more spread, proving my hypothesis wrong.

Another thing I noticed, or worked out rather was that 20% of boys lie below their lower quartile while 16.67% or girls lie below that same value meaning that boys data is more spread than girls below the lower quartile, proving my hypothesis right to an extent. It is a similar case when comparing the percentage of pupils above the upper quartile. Girls’ have 16.67% that lie above their upper quartile while boys have 50% which lie above the same value. This means that because they have a higher percentage it means that they could have a range of heights which means that the data could easily be spread out. To make it unbiased I also compared the percentage of girls above the boys’ upper quartile value, which still worked out to the same value of 16.67% while boys still had a higher value, of 20%, above their own upper quartile meaning that the data was more spread above the upper quartile for boys than it was for girls, proving my hypothesis right. Similar results were obtained for the grouped data so I felt no need to include it as the ungrouped data (for calculating percentages above lower and upper quartiles) already proved my hypothesis right and I would just be proving the same thing again (by using grouped data) using similar methods and obtaining similar results.

Overall I think my hypothesis has gone to plan and been successful in being proven right with the odd contradictions overshadowed by the numerous results that proved my hypothesis right.

...read more.

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