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 …