The PMCC was then calculated. It was 0.309855. This value was bigger than the critical value number for this sample size, so we can therefore be 95% certain of correlation between height and weight.
Conclusion
As is obvious from the trend line on the scatter graph (Appendix Two) it is possible to say there is some correlation. From our PMCC value it is possible to say we can be 95% certain of correlation between the data. We can therefore prove the hypothesis and say the taller you are the heavier you are.
PMCC value provides a basis set of values to which you compare the value you got for that particular data sample size. If the PMCC value your sample has is higher than the critical value of the chart, there is a sufficient relationship between the data to draw a trend line and say that there is correlation between the data. PMCC values are always between 1 and –1. If it is 1 or –1 there is perfect correlation between the data.
This can be used to prove the theory that if you had someone heavier than another person you can be 95% certain they will be taller than someone lighter than him or her. However, this was only a small sample so is not entirely accurate and cannot be used as a full proof for this hypothesis. If there had been any obvious anomalies they would have been removed and replaced but as it is possible to see from Appendix One, the sample. Anomalies may have occurred if the pupil had not answered the question properly or had mis-read the question. It is also possible that there were typing errors on the database we used, as this was secondary information. Being secondary information we cannot be fully sure of it’s reliability. This is only a snapshot of the whole population and cannot be used as a proven rule. It does however provide a basis for other theories and a general rule.
Hypothesis Two- “The older you are the taller you are”
In order to investigate this statement I will take a stratified random sample of boys and girls from years seven and eleven. There are different numbers from each year group so I will stratify the sample to get a full representative of the population. I will then use a calculator to generate the random numbers. Once this sample has been chosen I will calculate the mean, mode and median for each year. I will then draw a cumulative frequency curve for each year and calculate the inter quartile ranges and lower, upper and middle quartile values. Once I have done this, to represent the values, I will draw box and whisker plots.
Choosing the Sample
Year Seven- 282/452 x 60 = 37
Year Eleven- 170/452x 60 = 23
This Sample is shown as Appendix Three.
Proving The Hypothesis
Firstly the mean, mode and median were calculated for each year. These values are shown below.
Mean Height-- Y11= 1.67m,Y7= 1.55m
Mode Height---Y11= 1.65m,Y7= 1.42m
Median Height-Y11= 1.67m,Y7= 1.55m
I now drew a cumulative frequency curve, which is shown as Appendix Four. I drew both years on one graph so that it is possible to compare the data.
This is the table for height in meters.
Y11=
Y7=
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.
This sample was only of 60 pupils so can not be used as absolute proof to the theory “ the older you are the taller you are” but it can be used to prove this on a general basis.
Hypothesis Three- “Boys in year seven are heavier than girls in year seven”
To prove this hypothesis I took a sample of sixty students- thirty females and thirty males from each year group. This sample will be chosen at random using a random sampling button on a calculator. I will then calculate the mean, mode and median for this data and draw histograms to explore the hypothesis. This sample is shown as Appendix Six.
BOYS
Mean Weight= 49kg.
Mode Weight= 45kg.
Median Weight= 47kg.
GIRLS
Mean Weight= 45.7kg.
Mode Weight= 45kg
Median Weight= 45kg.
To draw a histogram I have calculated the frequency density.
BOYS
GIRLS
The histogram is shown as Appendix Seven. It has both years on it so that it is possible to compare the data.
Conclusion
As it is possible to see from the mean, mode and median for both the girls and the boys, all the values for the boys were higher than those for the girls. They had a higher average weight and a higher median and modal weight too. This means that the majority of boys are heavier than the majority of girls in year seven.
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.
