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" The taller you are the heavier you are."

Extracts from this document...

Introduction

                                                                                                                 Anna Cornock

Maths Coursework

Hypothesis One – “ The taller you are the heavier you are.”

To attempt to prove the above theory, a random stratified sample of sixty pupils across all the year groups. I stratified my sample, as there are uneven numbers in each year. I then generated random numbers using a calculator to choose the students. This is to eliminate bias and have a sample representative of the entire population. Once this sample had been chosen I calculated the mean mode and median for weight and height. I then drew a scatter graph for the data to show any relationship in the data between height and weight. I then calculated the Pearson Product Moment Correlation Co-efficient (PMCC) to see whether there was adequate correlation to draw a trend line.

Choosing the Sample

These values represent how many image00.png

Year 7- 282 pupils    282/1183 x 60=14                   of that year group are needed in

                                                                                  the sample.

Year 8- 270 pupils    270/1183 x 60=14

Year 9- 261 pupils    261/1183 x 60=13

Year 10-200 pupils   200/1183 x 60=10

Year 11-170 pupils   170/1183 x 60=9

This sample is shown as Appendix One.

Proving the Hypothesis

The mean, mode and median were calculated for both height and weight. These values are shown below.

Mean Height    = 1.63 m

Mode Height    = 1.56 m

Median Height = 1.62 m

Mean Weight   = 51.62 kg

Mode Weight   = 52.00 kg

Median Weight = 50.50 kg

A scatter graph was then drawn. See Appendix Two.

The PMCC was then calculated. It was 0.309855.

...read more.

Middle

Frequency

Cumulative Frequency

1.3-1.4

2

2

1.41-1.5

1

3

1.51-1.6

2

5

1.61-1.7

9

14

1.71-1.8

5

                          19

1.81-above

5

24

Y7=

Height/m.

Frequency

Cumulative Frequency

1.3-1.4

1

1

1.41-1.5

8

9

1.51-1.6

18

                          27

1.61-1.7

7

                          34

1.71-1.8

2

                          36                      

1.81-above

0

36

The upper, middle and lower quartiles where now calculated, which are shown on the graph, which is Appendix Four.

Upper Quartile Y11=1.7675m.

Median Quartile Y11= 1.675m.

Lower Quartile Y11= 1.61m.

Upper Quartile Y7=1.5955m.

Median Quartile Y7=1.555m.

Lower Quartile Y7=1.5m.

The interquartile ranges were now calculated. These are shown below.

IQR Y11= 1.7675-1.7=0.1575m.

IQR Y7= 1.5955-1.5= 0.0955m.

Box and Whisker plots were now drawn to show this data and the relationship between year eleven heights and year seven heights. This is shown as Appendix Five.

Conclusion.

It is possible to partially prove that older people are generally taller than younger ones but this is not always the case. There are always individuals, which vary from the average height group for their year. Although the box and whisker plots show that the year eleven students have higher quartile values than year seven pupils. In year seven the tallest person was a lot shorter than the tallest in year eleven but the shortest person was also shorter. This is could have been due to an anomaly in the data for year elevens which could have been caused by a birth defect or misunderstanding of the question or even a typing error as this was secondary data.

...read more.

Conclusion

        The histogram shows that whilst more girls weigh between 34 and 44 kg and 44 and 54kg, there are no girls weighing over 64kg yet there were four boys in the sample weighing more than 64kg. Also there is half the frequency of girls weighing over 54kg to 64kg than boys. More girls weigh less than boys and more boys weigh more than girls. It is possible to say that on average, boys in year seven weigh more than girls, but the frequency of girls weighing under 54kg is higher than the boys weighing under 54kg. Boys on average have a wider range of values than girls- not on the lower end of the scale but on the higher end. Some boys weighed over 64kg but no girls did for example.

        This is not entirely accurate as the sample was only of sixty pupils- thirty boys and thirty girls. This is only a small representative value for the whole year. Anomalies could have occurred through obese people or children with eating disorders. We did not look at height, so it is not possible to tell whether some people who weigh less are shorter than those who weigh more, though from Hypothesis One, this is quite likely.

        There is no definite proof that girls in year seven weigh less than boys in year seven but from my results and calculations, I would say that, on average girls in this year weigh less than boys.

...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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