What Statistics Is

A question at the farm shop

It is Emily Hartwell's first morning at Brookfield Growers, a co-operative of fruit and vegetable farms with a busy farm shop. Before she has even taken her coat off, two people have told her something with great confidence.

Ruth Oakley, who manages the farm shop, is worried. “A customer told me yesterday that nobody would recommend us any more since we changed the opening hours. She was very cross. Should we change them back?”

Ten minutes later Samuel Pike, who runs the orchard, leans in at the door. “Everyone knows the north block grows the biggest apples. Put the north block apples at the front of the display.”

Daniel Mercer, who keeps the co-operative's records, smiles at Emily. “Two claims before nine o'clock. Welcome to the job. One cross customer is a story, and ‘everyone knows’ is a feeling. Neither is evidence yet. Shall we look at what the records actually say?”

That, in a sentence, is what this course is about.

What statistics is

Statistics is the craft of learning from data. It has three parts, and you will practise all three:

• Collecting data in a fair way, so that it tells you about the thing you care about. Who was asked? How was it measured? Was anything left out?
• Describing data: turning a table of hundreds of numbers into a few clear summaries and charts. What is typical? How much do the values vary? Are there any odd ones?
• Drawing conclusions from data, while being honest about how sure you can be. A difference seen in a sample might be real, or it might be the luck of which cases happened to be measured. Statistics gives you tools to tell these apart.

The word also has a second, everyday meaning: a single number such as “65 per cent of customers would recommend the shop” is often called a statistic. In this course you will learn both to produce such numbers and to question them.

Why it matters

Statistics is not only for scientists. It helps with three kinds of situation that almost everyone meets every week.

Everyday decisions

Should you take a coat if the forecast says there is a 30 per cent chance of rain? Is a bus that is “usually on time” reliable enough for a job interview? Is a tomato variety that gave a bigger crop in one garden really better, or did that garden just have a sunny year? Each of these is a question about data and chance, and each has a sensible answer once you know how to think about it.

Claims in the news

News reports are full of numbers: “sales up 40 per cent”, “a new study links coffee to longer life”, “crime has doubled”. Some of these are careful and fair. Others compare the wrong things, pick a flattering starting point, rest on a handful of cases, or confuse two things happening together with one causing the other. By the end of the course you will know the questions to ask: out of how many? compared with what? could it be chance? who was measured?

Answers from AI assistants

More and more people ask AI assistants questions, and the answers often contain statistics: an average, a percentage, a claim that one thing is “significantly” better than another. These answers can sound authoritative while being wrong: a number may be made up, worked out incorrectly, or true of a different group from the one you asked about. An assistant is a useful helper, but it is not a source of truth. Knowing how an average, a percentage or a margin of error is calculated lets you check such an answer yourself, and the workbench in this course lets you do the recalculation in a few lines. Lesson 10.1 practises exactly this.

Data versus anecdote

An anecdote is a single story: one customer's complaint, a neighbour whose car never broke down, a relative who smoked and lived to ninety. Anecdotes are vivid and easy to remember, which is exactly why they mislead. The cross customer Ruth met is real, but she tells us about one person. The customers who were happy with the new hours had no reason to come and say so.

Data are observations collected in a planned way from many cases, so that each case counts once and nobody is left out just because they were quiet. (The word data is plural; one observation is a datum. Many people now treat it as singular, and both are accepted.)

In fact the farm shop did run a survey of 200 customers after the opening hours changed. Here is your first live workbench. Press Run and see what those customers said. (Every workbench on these pages runs inside your browser. You will learn exactly what each line means in the next few lessons; for now, just read the results.)

The table counts the answers: 130 of the 200 customers (65 per cent) said they would recommend the shop, and 70 (35 per cent) said they would not. So the cross customer is not alone, since about a third of customers would not recommend it, but “nobody would recommend us” is plainly false. Ruth now has something far more useful than a story: a number, out of a known total, that she can compare with next year's survey.

Checking a claim with data

Now Samuel's claim that the north block grows the biggest apples. The co-operative weighed 120 apples from the orchard's four blocks. The mean (the ordinary average: add up the weights and divide by how many there are) can be worked out for each block separately. Press Run:

Rounded to the nearest gram, the mean weights are: east 149 g, north 143 g, south 147 g and west 147 g. Far from growing the biggest apples, the north block has the lowest average of the four in this sample.

But notice how close the numbers are: the gap between the highest and the lowest is only about 6 grams, and a single apple can weigh 50 grams more than its neighbour. Is a gap that small a real difference between the blocks, or just the luck of which apples happened to be weighed? That is a genuine statistical question, and answering it properly needs ideas you will meet later in the course (spread in Module 3, samples in Module 7, tests in Module 8). For now, the honest summary is: the data give no support to Samuel's claim, and the four blocks look fairly similar.

The big questions this course answers

Over ten modules, Emily will learn to answer the co-operative's questions, and you will learn alongside her. The questions fall into a few big groups:

The course ends with a final project: a full investigation for Brookfield Growers, from question to written report.

How the workbenches and exercises work

Every lesson is built around live statistics workbenches like the two above. Each one understands a small, friendly language made for this course: one short command per line, such as mean(apples.weight). There is nothing to install, and every result appears in your browser straight away.

• Run (or Ctrl + Enter) works through the commands from the top and shows the result of each one underneath, including tables and charts.
• Reset puts back the commands the lesson started with.
• If a line has a mistake, the workbench stops there and explains in plain words what it did not understand, often suggesting the fix. The lines above still show their results.
• Commands that involve chance, such as tossing a simulated coin, give the same results every time you run the same commands, so what you see matches what the lesson describes.

From Lesson 1.2 onwards, each lesson ends with five exercises. Each exercise has its own workbench and a question from the co-operative, such as “show the average weight of the Russet apples” or “keep the number of late deliveries under the name late_count”. You type your commands and press Check my answer. The checker runs your commands and tells you whether the result is right. If it is not, it tells you what is still missing and may give a hint about a likely slip. There is usually more than one correct way to get an answer, and the checker accepts any of them. If you are stuck, Show solution reveals one correct answer, often with a note on what it means.

After the exercises comes a short quick check of four questions about the ideas in the lesson, and then a summary. This lesson has only the quick check.

Meet the people you will work with

Emily and Daniel will be with you throughout the course. Emily is new, curious and not afraid to ask “but what does that number actually mean?”. Daniel has kept the co-operative's records for years and has learnt, sometimes the hard way, which numbers to trust. Along the way you will also meet:

• Ruth Oakley, who manages the farm shop and its customer survey;
• Samuel Pike, who runs the orchard and has strong opinions about apples;
• Agnes Fairweather, who is running a trial of a new bean seed;
• Walter Bright, the delivery manager, and his drivers Albert, Beatrice, Cecil and Dora;
• and the two packing sheds, Hill and Vale, whose damaged boxes hold one of the course's best surprises.

Their records are the course's datasets: apples, rainfall, deliveries, a customer survey, the seed trial, sacks of potatoes, eggs, tomatoes, a blight test, packing boxes, and hedges and birds. Each one was built to show a real statistical idea clearly.

“So,” says Emily, looking at the two results on the screen, “the opening hours are not a disaster, and the north block apples are nothing special.”

“That is what these numbers say,” Daniel replies. “Next we will learn to read the records properly, row by row. Then you will be able to check claims like these yourself.”

Quick check

Four questions to confirm the main ideas. Choose an answer to see the explanation.

Found a mistake on this page, or something unclear? Report a problem and mention “Statistics Lesson 1.1”.