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  • Level: GCSE
  • Subject: Maths
  • Word count: 1912

Data Handling - GCSE Coursework

Extracts from this document...

Introduction

Maths Coursework – Data Handling

Hypothesis and Planning

My hypothesis is that there will be a relationship between pupils’ heights and weights. I predict that generally pupils who are taller will weigh more. In order to do this I am going to choose them from Year 11 because I think that this people are more likely to be more fully grown than any of the younger years and may be more in proportion.

In order to carry out my investigation, I should first select the data I will use. I’m going to do this randomly to make it fairer. I can use my calculator to help me choose using the random sample button. When I press shift, RAN#, it will give me a random number between 0 and 1. I need a random number between 1 and 84 for the boys, and between 1 and 86 for the girls, so I should multiply this number by 84 or 86 and round to the nearest whole to get my random sample number. I can then look for this number piece of data on my table.

Once I have collected the data I am going to put it into tally charts. Using a tally chart means it is easier to work out the totals for cumulative frequency graphs and is also easier to make a histogram from. A stem and leaf diagram will also make it easier to find the median of the data.

...read more.

Middle

h < 140

|||

3

140 < h < 150

||

2

150 < h < 160

||

2

160 < h < 170

||||||||||||

12

170 < h < 180

||||||||

8

180 < h < 190

||||

4

190 < h < 200

|

1

200 < h < 210

|||

3

I’m going to do the same for weight as well:

Boys

Weight, w, (kg)

Tally

Frequency

40 < w < 45

|

1

45 < w < 50

|

1

50 < w < 55

||||

4

55 < w < 60

0

60 < w < 65

|||

3

65 < w < 70

||

2

75 < w < 80

|

1

80 < w < 85

|

1

85 < w < 90

|

1

90 < w < 95

|

1

Girls

Weight, w, (kg)

Tally

Frequency

40 < w < 45

||

2

45 < w < 50

||

2

50 < w < 55

||||||||

8

55 < w < 60

|

1

60 < w < 65

|||

3

65 < w < 70

0

75 < w < 80

0

80 < w < 85

|

1

85 < w < 90

0

90 < w < 95

0

CombinedBoys& Girls

Weight, w, (kg)

Tally

Frequency

40 < w < 45

|||

3

45 < w < 50

|||

3

50 < w < 55

||||||||||||

12

55 < w < 60

|

1

60 < w < 65

||||||

6

65 < w < 70

||

2

75 < w < 80

|

1

80 < w < 85

||

2

85 < w < 90

|

1

90 < w < 95

|

1

I am now going to do histograms for these tally charts. I think it is good to do a histogram because it makes it easy for me to compare results and see which is the highest. I can compare height and weight on several separate graphs.

Histograms displaying my data in several different ways:

From these graphs I can first see that the higher numbers and lower numbers tend to be more rare. There are very few people who are above 180cm.Most people seem to be around the middle of my graphs. I’m going to work out the average height and average weight later using a stem and leaf diagram. I can also see that generally boys tend to be slightly heavier than girls, because there are more heavy boys in the 70kg – 90kg than in the girls. The modal class interval for height is 160 < h < 170, and the modal class interval for weight is 50 < w < 55.

So far I think I can say that generally those who are taller tend to be heavier, because the graphs seem very similar in shape (small at lower end, high in middle, small at higher end).

I’m going to make a frequency polygon so I can compare girls and boy’s weights and heights on one graph. This will help me try to prove my hypothesis.

You can see from the height frequency polygon that the two different genders follow the same pattern as the histograms. The middle values are much higher than the low values and high values. This again shows that my hypothesis may be true. They are also very similar – girls seem to be a little shorter in some places than the boys.

I’m going to do a stem and leaf diagram. Stem and Leaf diagrams make it very easy to find out the mean, mode, range and median of my results because they are set out easily.

Boys Height

Stem

Leaf

Frequency

130

2

1

140

0

150

1

1

160

5, 5, 7, 9

4

170

1, 2, 3

3

180

0, 1, 3, 4

4

190

7

1

200

3

1

...read more.

Conclusion

167

180

132

151

165

173

181

169

183

171

197

172

165

203

184

Weight

66

60

45

40

54

65

75

54

84

64

50

86

76

50

63

GirlsResults

Height

183

167

160

162

155

133

163

172

168

183

173

133

172

148

203

Weight

60

52

54

56

46

44

54

61

54

64

50

47

50

54

85

The line of best fit is useful for helping me work out averages. For example, I can work out that someone who is 150 cms tall might weigh 50kg. Of course this is only an estimate.

I’m going to make a cumulative frequency graph. Cumulative frequency graphs are good for display continuous data. The cumulative frequency is the running total of the frequency up to the end of the class interval. To find the cumulative frequency I first need to make a running total by adding the numbers.

CombinedBoys& Girls

Weight, w, (kg)

Frequency

Cumulative Frequency

40 < w < 45

3

3

45 < w < 50

3

6

50 < w < 55

12

18

55 < w < 60

1

19

60 < w < 65

6

25

65 < w < 70

2

27

75 < w < 80

1

28

80 < w < 85

2

30

85 < w < 90

1

31

90 < w < 95

1

32

Combined Girls & Boys

Height, h, (cm)

Frequency

Cumulative Frequency

130 < h < 140

3

3

140 < h < 150

2

5

150 < h < 160

2

7

160 < h < 170

12

19

170 < h < 180

8

27

180 < h < 190

4

31

190 < h < 200

1

32

200 < h < 210

3

35

From this I can work out which points I need to plot on my cumulative frequency graphs.

Weight: 45, 3  50, 6  55, 18  60, 19  65, 25  70, 27  80, 28  85, 30  90, 31  95, 32

Height:  140, 3  150, 5  160, 7  170, 19  180, 27  190, 31  200, 32  210, 35

Now I have finished all my graphs I think I can say that generally the taller someone is the more they weight. This is not always true as some people weight a lot but are quite short. However I think that my scatter graph especially shows a positive correlation, which tells me that my hypothesis was correct. My hypothesis was also that the Year 11’s would be more fully grown and I believe this is correct too.

...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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