AI and programming classes in Barnsley

The learner downloads the census table on car or van availability. Of Barnsley's 108,054 households, 22.7 percent have no car or van, 41.5 percent one, 27.4 percent two and 8.4 percent three or more. The simplest possible model of a household is just a set of probabilities for those four answers, and each place gives a different model: England's shares, Camden's shares, or a know-nothing model that says a quarter each. Cross-entropy measures how many bits, on average, a model needs to describe each Barnsley household. The lowest possible figure is Barnsley's own entropy, 1.8248 bits, reached only by a model that knows Barnsley's shares exactly.

The England model costs only 0.0011 extra bits per household, about 116 bits across the whole borough, because Barnsley's car ownership is very close to the national pattern. Camden, where 63.6 percent of households have no car or van, is a different world. A model trained there is so confidently wrong about Barnsley that it does worse than the model that knows nothing, 2.59 bits against 2.00. The extra cost is called the KL divergence, and it is not symmetrical: judging England by Camden's model costs 0.747 extra bits, but judging Camden by England's costs 0.624.

Two more lessons come from the table. A model that has never seen a household with three or more vehicles assigns that answer zero probability, and one such household makes its cross-entropy infinite; adding a tiny amount, 0.001, to every share fixes the crash but still costs 2.25 bits. And gradually mixing Barnsley's own shares into the England model, the simplest version of what AI builders call fine-tuning, lowers the score step by step from 1.8259 towards 1.8248. Each of these ideas applies directly to the language models behind chatbots.

Understanding what training data does to a model is a powerful reason for Barnsley teenagers to keep learning to code in 2026. The longer argument is in why teenagers should still learn to code in 2026.