Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 102 / 1 / a

The examination used separately emailed files. For this question a public Guerry data archive and its CSV mirror permit a documented reconstruction: retain the 85 records with a recorded region and select the specified columns. All six printed records match exactly, and each of the five regions has 17 departments. The numerical results below refer to that reconstruction; the remaining rows cannot be checked against the unavailable emailed file.

Treat department identifiers as labels and region as a categorical variable. The following summaries show the scale and spread of the quantitative variables:

A larger population-per-crime value means a lower crime rate, and a smaller wealth rank means greater recorded wealth. Donations are markedly right-skewed, as the large gap between mean and median and the upper tail indicate; rank is an ordinal measure rather than a monetary difference. For the ratio analysed next, the median is $2.683$, the interquartile interval is $[1.829,3.515]$, and the range is $[0.643,10.194]$.

Regional median ratios are $2.763$ in C, $2.502$ in E, $3.979$ in N, $1.373$ in S, and $2.937$ in W. The regional box plots and wealth-versus-log-ratio scatter plot in the figure expose this geographical contrast and an inverse association with wealth rank. North has the highest typical property-to-person crime ratio and South the lowest in the reconstructed data. These summaries are descriptive departmental comparisons, not causal or individual-level conclusions.