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  • Level: GCSE
  • Subject: Maths
  • Word count: 4014

Maths Statistics Coursework: Mayfield High

Extracts from this document...

Introduction

Math’s Coursework: Mayfield High

Mayfield High School is a secondary school of 1183 pupils aged 11-16 years of age. There are 603 male pupils and 580 female pupils at this school.

Year Group

Boys

Girls

Total

Year 7

151

131

282

Year 8

145

125

270

Year 9

118

143

261

Year 10

106

94

200

Year 11

84

86

170

For my Data Handling Coursework, I will be investigating a line of enquiry from the pupils' data. I have chosen to investigate the relationship between height and weight. One of the main reasons for choosing this line of enquiry is that my data will be Quantitative and Continuous, allowing me to produce a more detailed analysis rather than eye or hair colour- which are qualitative/categorical data where I would be quite limited as to what I can do.

Line of Enquiry: The relationship between Height and weight of pupils

If I was to make a hypothesis for the result, it would be: The taller the pupil, the heavier they will weigh.

For My coursework, I have chosen a sample size of 50 students; 25 of which will be girls and the other 25 will be boys. I have chosen to use this amount as I feel this will be an adequate amount to retrieve results and conclusions from, although on the other hand it may be a little number compared to the population size and hence could be unreliable.

To retrieve my data I am going to firstly use stratified sampling - A stratified sample takes a proportional number from each group in the population so that each group is fairly represented.  This is necessary when producing graphs or statistical calculations on more than one section of the population together.  Then once I’d got my stratified sample for

...read more.

Middle

Height Frequency Tables

Male Pupils

Female Pupils

Height, h (cm)

Frequency

Height, h (cm)

Frequency

120 ≤ h < 130

0

120 ≤ h < 130

0

130 ≤ h < 140

2

130 ≤ h < 140

1

140 ≤ h < 150

1

140 ≤ h < 150

4

150 ≤ h < 160

9

150 ≤ h < 160

8

160 ≤ h < 170

5

160 ≤ h < 170

11

170 ≤ h < 180

5

170 ≤ h < 180

1

180 ≤ h < 190

2

180 ≤ h < 190

0

190 ≤ h < 200

1

190 ≤ h < 200

0

Weight Frequency Tables

Male Pupils

Female Pupils

Weight, w (kg)

Frequency

Weight, w (kg)

Frequency

0 ≤ w < 10

0

0 ≤ w < 10

0

10 ≤ w < 20

0

10 ≤ w < 20

0

20 ≤ w < 30

1

20 ≤ w < 30

0

30 ≤ w < 40

3

30 ≤ w < 40

2

40 ≤ w < 50

9

40 ≤ w < 50

13

50 ≤ w < 60

4

50 ≤ w < 60

9

60 ≤ w < 70

4

60 ≤ w < 70

1

70 ≤ w < 80

0

70 ≤ w < 80

0

80 ≤ w < 90

4

80 ≤ w < 90

0

As I mentioned earlier both height and weight are continuous data so I cannot use bar graphs to represent it, instead I will have to use histograms as this is a suitable form of graph to record grouped continuous data. Before I produce the graph I am going to make a further hypothesis that;

"In general the boys will be of a greater height than the girls."

image00.png

Frequency Diagram of boys' heights

Frequency Diagram of girls' heightsimage01.png

As you can see in the two diagrams, there is an apparent contrast between the male and female heights. But the data is not presented in a practical way to perform a comparison, which is why I am going to present the two data sets on a frequency polygon.

image03.png

This graph supports my hypothesis as the male pupils heights reach up to the 190-200cm interval, whereas the female pupils’ heights do not have data beyond the 170-180 cm interval. The data, in the format of a stem and leaf diagram, is shown below. Stem and leaf diagrams show a very clear way of the individual weights of the pupils rather than just a frequency for the group-which can be quite inaccurate hence the reason for why I have chosen it.

Leaf (m) Females

Stem

Leaf(m)Males

1.2

                                        ,0

1.3

4,6,

                                6,3,0,0

1.4

1,

                           9,9,6,5,4,4,2,0

1.5

0,0,0,1,2,2,4,5,9

                      8,7,5,5,2,2,1,1,0,0,0

1.6

0,0,0,1,1

3

1.7

2,5,6,7,8

1.8

6,9

1.9

1

With these more detailed results, I can now see the exact frequency of each group and what exact heights fitted into each groups, as you cannot tell where the heights stand with the grouped graphs. For all I know all of the points in the group 140 ≤ h < 150 could be at 140cm, which is why I feel it is a sensible idea to see exactly what data points you are dealing with. I can also now work out the mean, median and range of the data.

Gender

Mean Height (m)

Modal Group

Median (m)

Range (m)

Male

1.624

150cm-160cm

1.61

0.57

Female

1.58

160cm-170cm

1.59

0.43

...read more.

Conclusion

 and from answering all of these other predictions I can confidently say that it is true. I have come to this conclusion based on all of the graphs, diagrams, tables and statements made. On the other hand there were cases where certain data undermined this prediction but that could have been because of the small samples I had allocated myself to obtain. When producing the random sample of 50, I felt that was a satisfactory amount to work with as picking up an analysis and producing graphs from this data was simple and done efficiently. If I were to repeat or further this investigation - I would definitely use a larger number of pupils for the as when the numbers of the school pupils were put on a smaller scale, I only ended up in some cases with a scatter graph with only 4 datum points upon for the year 11 students. To retrieve accurate results from this method of sampling, I feel it is necessary to use a sample of at least 100. Additionally to the stratified work, if I had a larger sample - I would also produce additional graphs, i.e. cumulative frequency/ box and whisker, as I feel that I could draw a better result from these as I felt the scatter diagrams I produced were rather pointless.

I feel my overall strategy for handling the investigation was satisfactory, if I had given myself more time to plan what I was going to do I think I would have come up with a better method and possibly more successful project. There is definitely room for improvements for my investigation - if I were to do it again I would spend a lot more time planning what I was going to do instead of starting the investigation in a hurry. Despite that I feel my investigation was successful as it did allow me to pull out conclusions and summaries from the data used.

...read more.

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