toronto’s human centre

Since it was trivial to calculate the centre of the city, I thought I’d do something a little more complex: calculate the centre of the city, weighted for population. I scraped the 2006 population data by ward from the City of Toronto: Ward Profiles pages; hooray for curl and regexes. Realising that I had no information on population distribution within wards, I made a good old engineering assumption: we could idealize the population as a point mass at the centroid of each ward, and then calculate the centre of mass by balancing moments around the X and Y axis. (I mean, c’mon – it’s the sort of thing we all think about daily … isn’t it? Guys … hello … anyone there?)

I’ll spare you the details until after the jump, but I calculate the human centre of Toronto to be at 43.717794°N, 79.390299°W – that’s in Blythwood Ravine, just south of Blythwood Road. We should have a picnic there …

I’ve transformed all the Open Toronto data into the one CRS, UTM Zone 17 NAD83(CSRS), aka EPSG 2958. Combining the ward centroids with the population data, we get:

ward xcentre ycentre 2006 population
1 613061.3 4844146.6 59830
2 614805.5 4840302.0 53660
3 615174.7 4834294.6 50415
4 617768.5 4836958.9 53275
5 618929.9 4832315.2 57260
6 619572.4 4829261.3 56620
7 617472.3 4844566.8 49165
8 620979.9 4846977.1 47895
9 622033.3 4843760.4 44920
10 624905.2 4846553.0 61580
11 620766.3 4838224.8 59870
12 622055.6 4840047.1 53755
13 622735.3 4834354.9 50640
14 625449.4 4833661.4 50640
15 624880.8 4841050.4 60545
16 627581.4 4842532.8 51790
17 624903.7 4837407.9 50830
18 625917.3 4834970.2 45620
19 627681.1 4834083.5 49845
20 629103.3 4834749.5 59545
21 626934.8 4838564.6 47085
22 629222.9 4839354.9 59905
23 627289.9 4847806.5 79435
24 630438.7 4850084.3 58805
25 630699.0 4844136.6 55420
26 632936.3 4841208.7 60585
27 630518.7 4836915.8 67840
28 631290.6 4833067.2 58920
29 633153.2 4838703.6 44420
30 633874.3 4835110.5 51235
31 636074.0 4839975.7 52430
32 636535.9 4836957.3 55410
33 632984.6 4848926.5 57350
34 634520.4 4844926.9 56895
35 639025.5 4841743.5 56750
36 641455.1 4841624.3 51390
37 638364.8 4845440.1 62325
38 641766.3 4847162.9 63310
39 635724.0 4851688.8 54545
40 636386.0 4848580.4 61140
41 639199.5 4851985.8 67325
42 644298.3 4853536.7 74075
43 644624.2 4847389.2 53480
44 648030.9 4849745.2 58235

To get the weighted average we simply divide the sum of (ward centre * population) by the sum of the population. Transforming the numbers back using invproj gets us the geographic coordinate of the centre point. Easy when you’ve no idea what you’re doing …

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