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:

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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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 ... [osm_map lat="43.717794" long="-79.390299" zoom="16" width="600" height="450" marker="43.717794,-79.390299" marker_name="wpttemp-red.png"] 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 ...