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• Level: GCSE
• Subject: Maths
• Word count: 1816

Gullivers theory - introduction

Extracts from this document...

Introduction

“… They measured my right thumb, and desired no more; for a mathematical computation that twice round my thumb is once round the wrist and so onto the neck and the waist…”

(Extract from Gulliver’s travels by Jonathan Swift)

• Investigate using any valid statistical method.

Aim

The aim of the coursework is to prove whether or not Gulliver’s theory is correct, (in accordance to the above extract), in reality.

Hypothesis

In my opinion, I do agree with the theory -to some extent- since, by measuring myself, I found the measurements of the body parts to be consistent with the other in agreement with the theory (± 4cm).

However since I’ve tested it only on myself for now, I cannot apply this rule to everyone since there are many factors to be taken into account.
And due to this fact, I believe that the theory is restricted to certain groups of people (e.g. those whose body parts are in direct proportion to the other) and may not necessarily comply with the majority as there are a number of aspects that can contribute to this.

One factor which can alter the consistency of the theory is gender. Boys tend to have a larger body build than girls and hence, I do not believe the theory to be true in this case.

Middle

Unfortunately year 4 girls are a total of 10 girls and so I will not be able to carry out my sampling method on them since my sampling size is originally 10 from each class anyways. The same situation has risen in year 4 and 11 boys.

Sampling method

• Simple random sampling is when a group of subjects (a sample) are chosen from a larger group (a population). Each subject from the population is chosen randomly and entirely by chance, such that each subject has the same probability of being chosen at any stage during the sampling process.
• Systematic sampling is the selection of every kth element from a sampling frame, where k, the sampling interval, is calculated as:

k = population size (N) / sample size (n)

Using this procedure each element in the population has a known and
equal probability of selection.

• Stratified random sampling is when a random sample of specified size is drawn from each stratum of a population.
There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is done by stratified sampling.

Conclusion

Gradient = difference in y = dy
difference in x    dx

I will also be working out the modal class (including the least common too), the median value and the mean. The modal class will be determined by the group having the highest frequency along with the least common class being the one with the lowest frequency.

The median {for the cumulative frequency diagram} will be calculated as:

The mean {for the histogram} will be calculated using the following formula:

Mean  x = fx

f

Another calculation I will be doing is
percentage error (including average percentage error) which will help me in deciding how close to reality the theory is; as any error will lead to inaccurate data and conclusions. So by using percentage error I will be able to determine how close to the actual or accepted amount I came.
To work out the percentage error I will use the following formula:

Plan
To see whether or not the theory is true.

• To do this I will investigate using any valid statistical method (explained above) which as said before will involve me interpreting, analysing and comparing graphs not forgetting calculations.
• I have already stated my aim and hypothesis as well as my selections i.e. choosing simple random sampling, specific graphs etc.
• I will now carry out my sampling method in order to get my required data and then plot it on various graphs. Calculations will then be done [e.g. gradient, mean, mode etc.] in order to see how valid the theory is.

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