# Statistics - Heights and Weight

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Introduction

Mohammed Pandor 10H Statistics Coursework

Due to the luxurious standard of living nowadays are British teenagers taller than they used to be?

In this Coursework I will complete a statistical enquiry. I will gain evidence to answer the question in the title by collect data using sampling, decide and justify which calculations to do and which diagrams to draw and interpret my results in this report.

From personal experience I feel that British teenagers nowadays are taller than they used to be. This is because my eldest brother who is 20 is taller than my father and my father is taller than my grandfather. I will try and find out that my prediction is true by comparing the results from this investigation with the results provided by the NHS of the average age a few 100 years ago

The three hypotheses that I predicted and will try to justify throughout the enquiry are as follows:

- Height and Weight has a fairly strong positive correlation because, generally the taller you get the more you weigh. I would expect the year 7’s to have a stronger correlation compared to the year 11’s.

- The year 7 girls will be taller than the year 7 boys. This is due to the girls starting puberty earlier therefore having a growth spur. The boys will start puberty later, with a few having gone through it or growing through it.

By year 11 the boys will be taller due to having already going through the stage of puberty. Most of the girls would have gone through puberty, therefore remaining a similar height as they were in year 7 whereas a few boys will still have to go through puberty.

Middle

For Spearmen’s rank of correlation I ordered the heights of the data for the sample of 25 from each subset. I then had to rank these data from 1 to 25 in ascending order. If the heights were the same than it would be a tied rank. After this procedure I highlighted the data and than ordered the weights from lowest to highest and than ranked them. d, d2 and Σd2 (the definition of the symbols are shown below). These calculations will allow me to Work through the formula which is also shown below.

The formula is

d = the difference in the rank of the values of each matched pair

n = the number of pairs

Σ = the sum of

The value of P will always be between -1 and 1. A negative answer indicates a negative correlation. -1 is a perfect negative correlation, 0 is no correlation and 1 is perfect positive correlation.

For the line of best of fit, as it was appropriate to draw, I had to work out a simple calculation as this would help me draw my line of best fit. This was the mean, with this I could work out the mid-point and draw my line of best through the centre of this point.

With this line of best, as seen on the graph, I made predictions. They were:

- An average year 7 girl with a height of 1.68 m will weigh 60 kg
- An average year 7 boy with a weight of 80 kg should be about 1.72 m tall.
- An average year 11 girl with a height of 1.8 m will way around 88 kg and
- A normal year 11 boy will weigh 100 kg if he was 20 m tall.

Conclusions

From the Scatter Graph I came to a conclusion that height and weight have a positive correlation.

Conclusion

- Boy’s height in year 7 will be normally distributed as only a few of them would have gone through puberty leaving the majority of them having to go through it.

Girls’ height in year 7 will be positively skewed as most of the girls having gone through puberty with a few of them having to go through it.

In year 11 both girls and boys height will be normally distributed as all the girls and most of the boys should have gone through puberty.

From hypotheses 1 I have gained evidence to suggest that weight and height is strongly correlated and this was as I predicted in the hypothesis.

As predicted the year 11 boys are taller than the girls however it is not easy to see who is taller in year 7 and therefore the first part of my hypotheses which comments on year 7 girls being taller is not true. This could be due to the set of data I collected.

The data for both year 7’s and year 11’s are normally distributed and this was not as I predicted in the hypothesis. In the hypothesis I mentioned that the girls height in year 7 will be positively skewed which it wasn’t.

From results of height and weight of children in 1837 I have come to a conclusion that the children nowadays are a lot taller than they used to be. The girl’s heights throughout the different ages in 1837 are similar to that of boys. The sheet with these data can be found in the Appendix.

This shows that British teenagers are taller than they used to be due to the luxurious living conditions.

As mentioned at the beginning of the report my results are reliable because I used a non-biased method of sampling which gave everyone the equal chance of being selected.

I did not encounter any problems throughout this investigation and therefore I am happy with the way I carried it out and would not change the way I would do things.

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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