Maths Statistics Coursework - GCSE Maths

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Guesstimate                                                 Joel Morrison

Maths Statistics Coursework

Guesstimate

Introduction

The title of my investigation is ‘Guesstimate’, as I will be looking at how accurate different people are at estimating. The aim of the investigation is to deduce estimating skills of pupils of different ages, abilities and genders. To do this I have created the following hypotheses:

1) The older you are, the better you are at estimating.

  1. The higher the band you are in, the better you are at estimating.
  2. Boys are better than estimating than girls.

In order to do this I will need to collect information for Key Stage 3, Key Stage 4 and Key Stage 5, and within the stages ability (band) and gender. I will collect this information from a database, which gives us: Key Stage, maths ability (higher, middle or lower band), gender and their estimates of an acute (17°), obtuse (147°) and reflex (302°) angle.

However, I will only be using the information for the obtuse angle, because the acute would be extremely small so people may guess zero, which would affect our results. Also, reflex angles could be mistaken for acute angles and vice versa, so people may not be giving an accurate estimate.

I will assume that the data is reliable, as I will eliminate bias from my sample by looking at the errors in guessing. To calculate percentage error I will use:

This will make it easier to see how far out the pupils were from guessing the correct angle, making it much easier to compare results. This means that 0% error will be a perfect estimate, so the higher the percentage error the worse the estimate.

I will use a stratified sample to

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This means that in fact Key Stage 5’s values are closely bunched (due to standard deviation) around a value that is further away from zero % error and therefore less accurate than Key Stage 4. Although Key Stage 4’s data is less consistent, it is less consistent around a value very close to zero, suggesting many pupils in Key Stage 4 guessed very accurately, on a contrary to my hypothesis.

The median and the skew of the box plots also seem to suggest this. Again Key Stage 4’s median is the closest to zero (-1.36), Key Stage 5’s median is further from zero (-4.76) and Key Stage 3 is further still (-6.16). This means on average Key Stage 4 were much more accurate than Key Stage 5, and the skew only emphasizes this point. We can see that in

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Key Stage 4’s box plot, there is a positive skew as the median (-1.36) is closer to the upper quartile (2.04). This means that the majority of the estimates were between -1.36% and 2.04% error with fewer below -1.36, giving incredibly accurate estimates. Whereas in Key Stage 5’s box plot, there is a negative skew as the median (-4.76) is closer to the lower quartile (-6.16). This means most of the estimates are between -4.76 and -6.16 and fewer above -4.76, extremely far off zero compared with Key Stage 4, and therefore the estimates are much less accurate. Of course, Key Stage 3 complied with the hypothesis, with a negative skew even more than Key Stage 5, with both the median and upper quartiles being -6.16.

Overall, my results do not comply with my hypothesis entirely. Key Stage 3 were by far the least accurate at estimating, which does conform to the hypothesis as they are the youngest.

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In conclusion, it is obvious that there is no concrete evidence that we can take away from this analysis, other than males are perhaps slightly better at estimating than females. We have seen no clear relationship between age and accuracy of estimation, nor between the seemingly most obvious relationship between maths ability and accuracy of estimation. It seems likely that, estimating an angle is exactly that – estimating. It has nothing to do with maths ability or age, but apparently gender does have some effect. It is just educated guesses that, according to this data, males are slightly better at.

However, there were still many things that would have improved the investigation were we to repeat it. For example, the sample size for much of the data may have been too small, so wouldn’t have allowed us to see a trend in the data. Increasing the sample size would give a much better representation of the population. As Key Stage 5 had a much smaller sample size and are all only in upper band ability making it hard to compare them, so this makes me question whether we should have included them into our investigation at all. They chose to do maths and perhaps it is unfair that none of the other students have actually chosen to do maths. We could also have looked at year groups instead of Key Stage, as it would probably be easier to spot a trend if there were more categories to work from. Doing this would allow us to draw many more box plots to investigate in much further detail.

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