Harry Shannon
There’s a story about a museum guide, who was showing visitors around the exhibits. Coming to an ancient artifact, the guide stated: “This one is five million and three years old.” One curious visitor asked: “How can you be so accurate with the dating?” The guide answered: “Well, when I became a guide, the museum director told us that it was five million years old, and that was three years ago.”
I was reminded of this while I was reading Jeremy Black’s A Brief History of Britain 1851-1950. Black provided data on how industry in Britain developed in the 19th and early 20th Centuries. He gave the number of tons of coal production in various areas and tons of ships built in several cities at different dates, and then in brackets gave the conversion to tonnes (see some of the data in the Table below).
But the way he did this suggested he is innumerate.
First, since 1 ton is just about 1.016 tonnes, there is really no point in showing the converted values. If you know the number of tons, you pretty much know the number of tonnes; it’s just a little more.
Second, he couldn’t even do the simple multiplications without a mistake. He reported that 67 tons was 69 tonnes. It isn’t – it’s 68 (to the nearest whole number).
Third, even though some numbers of tons were given to the nearest 1000, he showed the number of tonnes to an exact integer. So 190,000 tons was stated to be 193,048. Now that is correct. But the figure of 190,000 is clearly an approximation. You can’t magically improve the precision when you convert the number to a different unit.
Likewise, he converted ‘over 60,000 tons’ to ‘c. 61,000 tonnes’. But ‘over 60,000’ covers a lot of possibilities. All you can say is that the number of tonnes is over 61,000.
Fourth, giving too many significant digits* actually makes it harder for readers to grasp the impact. The extra digits clutter our minds with irrelevant information. Knowing that a number of tonnes (for shipping built in Clyde in 1881) is 346,471 tells you almost nothing that the number 346,000 doesn’t already tell you. And this is especially so when (as it was for Black) your reason for quoting the number was to compare it to the value in 1914 – which was 769,000.
You can avoid these errors by following some simple principles.
- If your purpose is to make comparisons between, say, measures at different times, you only need to report the data in one unit.
- If you make a conversion, you cannot have more significant digits in the new value than you had in the original value.
- For presentations, try to report the final numbers to just two significant digits (or maybe three).
- Double-check your calculations
Data from Jeremy Black’s A Brief History of Britain, 1851-2010
*You can find a nice explanation of significant digits here