Statistics & Data Science · Essentials

A cook tastes one spoonful and decides about the whole pot. Every survey, poll and medical trial does the same thing with people. This chapter shows how a small sample can speak for a large population, and how it goes wrong when the sample leaves people out. You will choose samples fairly, judge the margin of luck in a poll, and design a study that can tell a cause from a coincidence. Every idea starts from a made-up data set or a simulation, and short Python programs do the counting.

Thirty students write down how long their journey to school takes. A list of thirty numbers says very little. A picture of the list says a lot: where most values sit, how far they spread, and whether a few lie far away. In this chapter you draw histograms and box plots, read the shape of a distribution, find outliers with a clear rule, and measure spread with the standard deviation. You also learn to compare a value with its group through a z-score. Small Python programs do the counting, so you can spend your time on what the numbers mean.

A bus is late on some days and on time on others. A coin lands heads five times in a row. A game at a fair costs a coin to play. How likely is each thing, and what happens in the long run? This chapter finds probabilities from data and from equal chances, and checks every rule with a simulation. You will add and multiply chances, draw probability trees, read two-way tables and work out whether a game is fair. The Python is short and explained line by line.

How many brothers and sisters does a student picked at random have? How many seeds in a packet will grow? How tall is the next person through the door? Each answer is a number that changes by chance, and each follows a pattern that we can describe. This chapter turns chance into numbers. You will build a probability distribution, find its long-run mean and its spread, count successes with the binomial model, and work with the bell-shaped normal curve and its areas. Every idea is met first in a made-up data set or a simulation, and short Python programs check each result.

Do students who practise more type faster? Is a mountain town cooler than a town by the sea? When we measure two things about each person or place, a scatter plot shows how they move together. This chapter puts a number on that pattern, fits the line that predicts one measurement from the other, and then asks the hard question: does one thing really cause the other? Every idea starts with a made-up data set or a simulation, and short Python programs do the arithmetic. It suits a curious student from Class 9 onwards and any adult who reads graphs in the news.

A poll asks a thousand people and speaks for a whole country. How can a small sample say anything sure about millions? The answer is that chance, which makes every sample a little different, also follows rules. In this chapter you watch samples scatter, measure how far a sample is likely to miss, and turn that into an estimate with a margin of error. Then you test an idea: is a coin fair, does a new method help? Small simulations in Python do the heavy work, so you can see each idea happen before you name it.