Interrogating a real dataset: traffic, and rainfall

0:00Here is a real dataset, and it is not a friendly one. The number of objects launched into space, every year, for thirteen years. Four series. A world total, and three countries: the United States, China and Russia. Before a single conclusion, notice what the figure hands you. A title. A unit - objects, not launches. Years along the bottom. And a line saying where the numbers came from. That last one is the part everybody skips, and it is the only thing on the picture that lets you find out how the numbers were made.

0:40A figure without it can be read. It cannot be checked. So, pass one. What is given. The upright axis counts objects. The bottom counts years. Two of the four series are drawn at every year; the other two only where they could be read. And the unit is doing more work than it looks. Objects, not launches. One rocket carrying forty small satellites counts forty, and not one. Get that wrong and every number on the picture means something else.

1:16Only now, pass two. What it means. Which brings the real question. Where does a number like this come from? Somebody has to be told about every launch, and somebody has to count the objects it carried. States report their launches to an international register, and the register adds them up. That is why the series exists at all. It is not a measurement of space. It is a count of reports.

1:47And a count of reports has an obvious weak point: anything nobody reported is not in it. Hold that thought. Here is a check almost nobody runs. Add the parts and compare them with the whole. In the last year, the three countries read two thousand two hundred and eighty, three hundred, and one hundred and fifty. Together, two thousand seven hundred and thirty. The world line reads two thousand eight hundred and seventy.

2:20A shortfall of one hundred and forty. So other countries are launching things, and this figure does not show them. Notice how small that gap is - about one part in twenty. Small enough to miss, and large enough to matter. Nearly complete is not complete. One more reading before the hard part. Look at the United States line at its two last steps. From the third year from the end to the second, it climbs two hundred and ninety-five.

2:54From the second to the last, it climbs thirty-five. You did not need either number to see that. The first segment is steep and the second is nearly flat, and steepness is the size of a change. Both are rises. The line went up twice. It just went up very differently. Now four statements about this figure, and here is the thing most people get wrong. There are not two verdicts. There are three.

3:24SUPPORTED - the figure shows it. CONTRADICTED - the figure shows the opposite. And NOT ADDRESSED - the figure says nothing either way. Statement one: the world count rose every year. Contradicted. It falls in the last year, from two thousand nine hundred and ten to two thousand eight hundred and seventy, and it dips three other times earlier on. A rising trend and rising every year are different claims.

3:55Statement two: the United States launched about three quarters of the world total in the last three years. Supported - and supported in each of the three years separately, at about seventy-eight, seventy-seven and seventy-nine per cent. Statement three. Kenya launched nothing in these thirteen years. Watch what happens if you only have two verdicts. You look at the figure, you see no Kenya, and you tick TRUE. But there is no Kenya line to see. The figure plots three countries and a world total. Everything else is outside what it reports.

4:37The right verdict is NOT ADDRESSED. Whatever the truth about Kenya is, you cannot get it from here. And notice the trap in the arithmetic we just did. The shortfall proves other countries launched something. It cannot tell you which ones. Absence from a figure is not evidence of absence in the world. Statement four is different again. Find two consecutive years where the world count at least doubled. One pair is easy. Six hundred to one thousand two hundred and seventy-five is a ratio just over two point one.

5:18But how precisely can you read a drawn line? Say twenty-five objects either way. Then that ratio is somewhere between two and about two point three. Even at its worst it doubles. Supported. Now an earlier pair: two hundred and forty-five to four hundred and eighty-five. That is one point nine eight. Just short. Except with the same twenty-five either way, it runs from about one point seven to about two point three. It straddles the bar.

5:52So the honest answer is a fourth verdict: this figure cannot settle it. Measure it yourself and let the class disagree - that is the lesson, not a tidy tick. A second dataset, and a decision worth arguing about. Monthly rainfall for six places: three on a western coast, three on an eastern one. Both figures are drawn to the same top, nine hundred millimetres. So they are honestly comparable, and one thing leaps out: the wettest month of one western place, eight hundred and seventy-eight millimetres, is larger than any month at any of the three eastern ones.

6:38Across the year the west takes six thousand nine hundred and twenty-seven millimetres to the east's three thousand seven hundred and sixty-seven. But look at the cost. The tallest eastern mark is three hundred and sixty-five. The eastern figure never even reaches half its own height, so three very different rainy seasons are squashed into the bottom strip. One decision bought the comparison and sold the detail. Would you have made it?

7:12And what IS one of those marks? Eight hundred and seventy-eight millimetres of July rain. It is not what fell last July. It is several Julys, averaged. Here are the five that made it: nine hundred and five, eight hundred and twelve, nine hundred and forty, eight hundred and fifty-eight, eight hundred and seventy-five. Not one of them is eight hundred and seventy-eight. The plotted value is a July nobody lived through.

7:44That is not a flaw. It is what the word average means, and it is the answer to how were these numbers made. One more thing the six curves agree on: the first three months are dry everywhere. The wettest of any of them is eighty-five millimetres - less than a tenth of that one July. Third dataset. Rainy days a month, four places, and one row left completely blank.

8:14The blank one is already drawn on the graph. So read it off: one, one, one, one, one, four, ten, ten, four, one, none, one. Thirty-five rainy days a year. The three written rows come to a hundred and twelve, a hundred and twenty-six, and forty-two. So which place has the most rainy days, and which the fewest? The most is clear. The fewest is not. Thirty-five against forty-two is seven days apart, on readings taken off a drawn line. Close enough that you must read carefully rather than glance - and close enough to say so out loud.

8:58Two last figures, and two last ways to be wrong. Households, by the source they mainly light with. Someone says: in that middle year, a tenth of urban households used electricity. There IS a tenth on that panel. About eight in a hundred. But it is on the kerosene line. Electricity reads ninety-two. The right number, off the wrong line. Contradicted - and the most instructive kind, because the reader did measure something.

9:30Look also at the small print: this is a share by PRIMARY source. In the first year the two lines add to ninety-five, not a hundred, and the missing five are households lighting some other way. Last figure. Average hours a day spent playing, by age. Somebody claims every rural fifteen-year-old plays an hour and a quarter. But four children averaging an hour and a quarter can be four children playing an hour and a quarter each - or three playing nothing and one playing five hours. Same average.

10:09An average curve cannot support a claim about anybody in particular. Not addressed. Supported. Contradicted. Not addressed. And sometimes, honestly, this figure cannot settle it. Four boxes, and the last two are the ones that keep you truthful.