Online coding and Python classes in Ilford

The learner downloads Code-Point Open, the Ordnance Survey's free postcode file, and keeps the 1,325 postcodes in the IG1 and IG2 districts. Each has an easting and a northing in metres; for Ilford the eastings average 543,986 m. The task is to measure how spread out the postcodes are, the variance of their coordinates, three ways. First, the textbook one-pass formula: average of the squares minus the square of the average. Second, the two-pass method: find the average, then average the squared distances from it. Third, Welford's online algorithm, which updates a running mean and a running sum of squared differences one value at a time. Each is run in 32-bit floating point, the compact number format common on graphics cards, and checked against an exact answer from Python's fractions.

The textbook formula is wrong by a factor of three on the eastings, because squaring numbers around 544,000 gives about 296 billion, far more than a 32-bit float can hold precisely, and the tiny true spread is lost when two such giant numbers are subtracted. On postcode sector IG1 1, 220 postcodes, it goes further and returns a variance of minus 98,304, a mathematical impossibility; the true value is 158,907.5. Welford's method never forms those giant squares, so it stays within a small fraction of a percent while reading each value only once. In Python's ordinary 64-bit floats the textbook formula happens to survive on this data, off by only 0.00005, which is exactly why the problem goes unnoticed until someone switches to a smaller number type.

Checking that answers are even possible lets Ilford teenagers trust code for the right reasons, a solid reason to learn Python in 2026. The longer argument is in why teenagers should still learn to code in 2026.