• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Gullivers theory - introduction

Extracts from this document...


“… 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.


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


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.

...read more.


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.

...read more.


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 = fximage01.png


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:



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.

...read more.

This student written piece of work is one of many that can be found in our GCSE Miscellaneous section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Miscellaneous essays

  1. Maths Statistics Coursework

    There is a clear pattern to see when all the standard deviations are shown: This shows that as we go up in ability, standard deviation lowers and therefore consistency increases. Again, though, age (Key Stage) does not seem to affect consistency considerably.

  2. The investigative task. Do housewives or working adults have a faster working pulse rate?

    Working in a office meant not doing much moving, although there were some with really active jobs like a fitness coach but there wasn't enough working adults with a active job to make the pulse rate average go higher, there was just too many boring working adults in a office.

  1. The aim of the project is to investigate the correlation between multiple sets of ...

    The above graph contains unedited data from all of the children aged 9-15 who said that they travel to and/or from school using an "other" method (other than the suggested methods of transport from the survey). The data must be changed using the correct age ratios before it can be

  2. Mathematics Handling Data Coursework: How well can you estimate length?

    I must also acknowledge the fact that I decided on boundaries for what I would count as acceptable values. I counted rogue values as under 1.00m and over 2.00m, but if I had raised or lowered the boundaries my mean and standard deviation calculations may have been affected, if only slightly.

  1. maths estimation coursework

    add up to 69 and 71, so my sample of the population amounts to 140 people. I have now determined that this is a representative stratified sample and I will proceed to use at least 140 people in my sample for my investigation.

  2. Statistics coursework. My first hypothesis is that people with a smaller hand span ...

    A 10 centimeter ruler is not long enough; most people don't have quick enough reaction times to react before the ruler has passed through their hand. Instead of using a 10 cm ruler, for my experiment I will now use a 30 cm ruler.

  1. Investigation into 100m times and long jump distances

    11.6625 12.94625 11.0625 1.45 1.525 2.4 Q3 + (1.5 x IQR) 26.1625 20.55625 19.7625 4.25 4.525 5.3 Outliers None 20.7, 21.7 20.7, 22.8 None None 1.5, 1.3 From the table above, there are a few entries in years 9

  2. Statistical Experiment Plan to investigate the ability to estimate 30 and 60 seconds.

    I shall do the outlier test on my sample. To do the outlier test I will take away the upper quartile from the lower quartile to find the interquartile range (IQR). Then I will add 1.5*IQR to the Upper quartile to get my upper bound. To calculate my lower bound I will do the Lower Quartile take away from 1.5*IQR.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work