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114 bytes added ,  18:22, 7 March 2021
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In the figure the results for Maroc are shown.
 
In the figure the results for Maroc are shown.
 
[[File:TransportationSizeMaroc.png|thumb|center|The population road-distance weighted transportation size of Maroc]]
 
[[File:TransportationSizeMaroc.png|thumb|center|The population road-distance weighted transportation size of Maroc]]
The cumulative population 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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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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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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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.
    
The function to fit must behave nicely with extrapolations. This excludes complex functions with many parameters. Or functions which behave not regular outside the fitted points (polynomials).
 
The function to fit must behave nicely with extrapolations. This excludes complex functions with many parameters. Or functions which behave not regular outside the fitted points (polynomials).
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This leaves the following functions:
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This leaves the following functions in Google Sheets:
 
* linear - results in average values;
 
* linear - results in average values;
 
* logarithmic - results in smaller values;
 
* logarithmic - results in smaller values;
 
* power functions - results in larger values, but goes through (0,0);
 
* power functions - results in larger values, but goes through (0,0);
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In order to get a handle on this choice, a plot has been created for the departments in France. With a population fraction of 80%, the power function gives the best fit.
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In order to get a handle on what is the best function, a plot has been created for the departments in France. With a population fraction of 87%, the power function gives the best fit to the data, using all points.
    
== Result ==
 
== Result ==
3,393

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