Coding and AI classes in Ecclesall, Sheffield

The learner downloads the ward's resident count from Nomis, uses the ONS lookup to find its 63 output areas, and takes each area's population-weighted centre point and resident count. The centroid is just the weighted average of those points. The geometric median is the point with the smallest total distance to everyone; Weiszfeld's algorithm finds it by starting at the centroid and repeatedly re-averaging with each area weighted by residents divided by its current distance, so nearby areas count more each round.

The two points are 61.1 m apart, yet the average walk differs by less than a metre, about 0.1%. Near its minimum the total distance is almost flat, so many nearby points are nearly as good. The same happens across the whole city: using all 1,829 Sheffield output areas, the median lies 414 m from the centroid and saves only 0.31% of average distance. Where the median earns its keep is robustness. Add a hypothetical block of 3,000 people 3 km outside the ward and the centroid lurches 385.0 m towards them, while the median moves 182.0 m. A single faraway group pulls an average much harder than it pulls a median.

An Ecclesall teenager who asks what an optimum gains, and what could knock it over, reads AI output with a sharper eye, and coding is how that eye is trained. The longer argument is in why teenagers should still learn to code in 2026.