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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.
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 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.
I found the sampling method sheet particularly useful using our school as an example and discussing the strengths and weaknesses of each.
For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). Experimental probability and the importance of basing this on a large trial is also covered.