Statistics — mean, median and spread

Five colleagues' monthly commuting costs: 200, 250, 250, 300, 3000 (one of them flies). The mean is 800 kr — but nobody gets anywhere near that. The median (the middle value) is 250 and describes the group better. An extreme value drags the mean but not the median.

Spread says how spread out the values are. Two classes can have the same average grade, but one has everybody in the middle and the other has half at the top and half at the bottom.

For the values x₁ … xₙ:

• Mean: x̄ = (x₁ + … + xₙ) / n
• Variance: s² = Σ(xᵢ − x̄)² / n (population variance)
• Standard deviation: s = √s²

Example [2, 4, 4, 4, 5, 5, 7, 9]: x̄ = 5, the squared deviations sum to 32, s² = 4, s = 2.

Why in AI? A model's errors are a dataset. The mean error says how good it is on average; the spread says whether it is evenly good or occasionally catastrophic. And normalising the data (subtract the mean, divide by s) is often the very first step before training.