Turning an argument into a question you can settle with data

0:00Two children in a class are arguing. Navya says cricket is the most popular game in the class. She is quite sure about it, and her own favourite happens to be cricket. Naresh plays cricket sometimes, but he likes hockey best. And he says something far more useful than no it is not. He says: I am not sure how we could find out. That sentence is where this whole chapter starts, and it is a better move than it looks.

0:31Because the two of them could assert at each other all afternoon and get nowhere. Neither one can win by saying it louder. So your book stops and defines a word. Data. And the definition is broader than you might expect. Data is facts, numbers, measurements or observations — anything recorded that tells you something about things. Not only numbers. The book's very first example is a list of colours.

1:03Red, blue, green, blue, red. That is data, and there is not a number in sight. So is a column of weights. So is a list of games. If you have written down something true about each of a set of things, you have data. The counting comes afterwards. Now look carefully at what Navya actually claimed. She said cricket is the most popular game in the class. That is not a claim about Navya. It is a claim about thirty-one people.

1:37And here is the mistake worth naming, because very nearly everybody makes it. Her own favourite is cricket, and she is treating that as evidence. It is not evidence. It is one entry. In a class of thirty-one, Navya's opinion counts once. Exactly as much as everybody else's, and not a bit more. So the argument has to turn into a question. What would we actually have to know? And before you collect anything at all, you have two things to settle.

2:12Who are we asking, and what are we writing down? Who: every classmate. All thirty-one of them. Each one asked once. What: the name of their favourite game. One game each. That sounds obvious. It is also the part people skip, and skipping it is how surveys go wrong. If you go and ask a hundred strangers instead, you have not got a better answer to this question. You have got the answer to a different question.

2:44So they go and ask. And here is what comes back. Thirty-one names, each with a game written beside it, in the order the answers arrived. Hockey. Cricket. Basketball. Cricket. Football. Volleyball. Hockey. Badminton, and on it goes. Six different games turn up altogether: cricket, hockey, football, badminton, basketball and volleyball. And that is a real, honest data set. Every single entry is a true fact about a real person.

3:18So now look at it, and tell me which game wins. Go on — the answer really is in there. You cannot, can you. Not just by looking. And your book stages that beautifully. Navya announces that now she can find the winner — and the other children say, plainly, that they cannot see it in there. Which is the whole point of this section. You have got the data. The data contains the answer. And you still cannot read it.

3:51Because your eye cannot hold six running totals while it scans down thirty-one lines. Mine cannot either. So data and a readable answer are two different things, and the gap between them is what the rest of this chapter is about. Right. Let's count it properly. Go through the list once, and drop each answer onto a heap. Hockey. One, two, three… eight of them. Basketball: six. Cricket: six. Volleyball: five. Football: four. Badminton: two.

4:26Eight, plus six, plus six, plus five, plus four, plus two. Thirty-one. Everybody is accounted for — which is your check that you have not dropped anyone or counted anyone twice. And now you can read the answer in one look. Hockey wins. So what has actually been settled here, and what has not? Settled: in this class, hockey is the most popular game, with eight. Also settled, and worth pausing on. Navya was wrong.

5:00And not merely wrong about the winner. Cricket got six — but so did basketball. So cricket is not even second on its own. It is joint second. The person who was most confident had the least evidence, and this chapter is built that way on purpose. Not settled: anything at all about the school. Or about children in general. Or about next year. Thirty-one people answered, so the conclusion is about those thirty-one people. Stretching it further is the commonest mistake made with data anywhere.

5:39Next, your book introduces Pari, who has four questions, and asks which of them need data collecting. One. What is the most popular television show among my classmates? Two. On what date did the first person walk on the Moon? Three. How much water is being wasted in my neighbourhood? Four. What is the capital city of Japan? Have a think about which two of those need you to go out and gather something, and which two you could settle without leaving your chair.

6:12Here is the test, and it is a single question. Is the answer already written down somewhere — or does it exist only in things nobody has measured yet? The Moon landing has a date. It is recorded. You look it up. And asking thirty-one classmates is not merely unnecessary, it is worse: it measures what your classmates believe, not what happened. Same with the capital of Japan. Survey that and you might get the wrong answer by majority vote.

6:46But nobody has written down what your classmates' favourite show is. That fact does not exist anywhere until you ask. And nobody has measured your neighbourhood's wasted water. Somebody has to go and look. Recorded, or not yet recorded. That is the whole sorting rule. So your book gives you three of these to do. One. Your own class's favourite game. Guess first, then collect — and find out whether you were Navya.

7:19Two. Count the trees you pass between home and school. A two-column table: kind of tree, and how many. Three, and this one is my favourite. Take a piece of newspaper and count how many times each of five letters appears. C, e, i, r and x. And your book says something surprising about it. Almost everyone who does this ends up with the same order. Rarest is x. Then c, then r, then i. And the commonest, by a very long way, is e.

7:54I checked that on the scripts of every video in this series so far — about two hundred and twenty-seven thousand letters — and it comes out in exactly that order. Which tells you something. That data is not about your newspaper. It is about English. So look at what has happened here. An argument became a question. The question named a group, and named what to record. The asking produced a list. And the list produced a count that settled the argument.

8:29Four steps, and the mathematics started at step one — before a single number existed. But we are not finished, because that middle stage was painful. Thirty-one lines that nobody could read. Next time, the tools that fix exactly that. How to organise a raw list so that the answer becomes visible — starting with the tally mark, which is a far cleverer invention than it looks. And after that, how to draw it, so that somebody can take the answer in from across the room.