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813 bytes added ,  18:30, 9 March 2021
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The cumulative population road-distance weighted distances are plotted against the cumulative population ratios. Each added city adds a point, increasing the cumulative population ratio and the cumulative distance. If the cumulative population ratio is 1, we have covered the entire population. And the corresponding cumulative distance is the value we are looking for.
 
The cumulative population road-distance weighted distances are plotted against the cumulative population ratios. Each added city adds a point, increasing the cumulative population ratio and the cumulative distance. If the cumulative population ratio is 1, we have covered the entire population. And the corresponding cumulative distance is the value we are looking for.
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=== Fit function ===
 
Adding all the cities is to much work. Instead of adding all the cities, we could fit a line to the data of a few city points. The cumulative distance of the fit at a population ratio of 1, is then again the value we are looking for.
 
Adding all the cities is to much work. Instead of adding all the cities, we could fit a line to the data of a few city points. The cumulative distance of the fit at a population ratio of 1, is then again the value we are looking for.
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As can be seen from the graph the slope does not stay constant as more and more departments are added. At this close inspection the power function fit is better. The linear fit to the slope (not the original data) confirms this conclusion and provides a better fit.
 
As can be seen from the graph the slope does not stay constant as more and more departments are added. At this close inspection the power function fit is better. The linear fit to the slope (not the original data) confirms this conclusion and provides a better fit.
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=== Accuracy ===
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The conclusion is that the power function gives the best result for a country when we have 100% of the data, i.e. up to a population ratio of 1. At what population ratio do we get an estimate of the weighted country size that is good enough. We can define good enough as within 10%.
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So for France this will be at 371 ± 37. The evolution of the size estimates as departments are added and the population ratio increases is shown below.
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[[File:FranceDepartmentsSizeEstimateEvolution.png|thumb|center|The evolution of the weighted size of France, using the departments.]]
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The red dot shows where the estimate is within 10% of the final value. So this occurs well above a population ratio of 50%. If we accept an error of 20%, a population ratio of at least 30% is required.
    
== Result ==
 
== Result ==
3,393

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