Math for AI (Statistics and Probability)
Patterns, statistics and probability: the maths that lets AI learn and predict.
1Patterns: the heart of AI
AI is very good at one thing: finding patterns in numbers and pictures, then using them to predict. To a computer, even a picture is just numbers. Solve the pattern puzzles, then draw a picture and see its numbers.
To a computer, a picture is a grid of numbers. Tap or drag on the grid to draw. Each square is 1 (ink) or 0 (blank).
2The maths behind AI
Four branches of maths power AI. Statistics helps explore and summarise data. Linear algebra stores data as tables of numbers (vectors and matrices) and works with them. Probability measures how likely things are, so AI can predict. Calculus helps a model improve itself, step by step, while it trains.
3Statistics in real life
Statistics is the science of collecting, organising, analysing and interpreting data to make decisions. It is used in disaster management, sports, disease prediction and weather forecasting. Try it yourself: collect data by spotting cars, then organise and interpret it.
Car spotting. Press Start. Each time a car passes the dashed box, tap its colour. Then compare your tally with the real count.
4Describing data: mean, median and mode
Three numbers summarise a set of data. The mean is the average (add all values, divide by how many). The median is the middle value when the data is sorted. The mode is the value that appears most often. Drag the dots to see how each one changes.
Marks of a group of students (out of 20). Drag any dot to change a mark. Watch the mean, median, mode and spread respond.
5Probability: how likely is it?
Probability tells us how likely an event is, as a number from 0 (impossible) to 1 (certain). When all outcomes are equally likely: P(event) = number of favourable outcomes ÷ total number of outcomes. Run experiments and watch the results get closer to the theory as the number of trials grows.
6Types of events and uses of probability
Events can be impossible (probability 0), unlikely (less than 1/2), equally likely (exactly 1/2), likely (more than 1/2) or certain (probability 1). Probability helps in sports, weather forecasting and traffic estimation, and AI uses it to make every prediction.