Maths on the Back of an Envelope: Clever Ways to (Roughly) Calculate Anything by Rob Eastaway

Author:Rob Eastaway
Language: eng
Format: epub, pdf
Publisher: HarperCollins
Published: 2019-09-18T23:00:00+00:00

SPOTTING TRENDS

Much of our modern life is underpinned by statistics. They dominate our news, and we use them to form opinions, make judgements and, most importantly, make decisions. It’s a statistician’s job to wade through data and to spot important patterns and connections. And in an era where ‘big data’ is used to help advertisers, political parties and other institutions to understand our behaviour in frightening detail so that they can understand and perhaps influence us, it should come as little surprise that the best statisticians can earn huge salaries.

The maths involved in statistics can get quite advanced. If you’ve got a set of data (such as the fictitious points in the graph below) and are looking for the straight line that most tightly passes through it (the so-called ‘best fit’), there are sophisticated mathematical techniques you can use to find it.9 But in many cases, the human eye is good enough. A bit like in a spot-the-ball competition, I’ve used my judgement, and a hunch, to draw a straight line through the points below. It suggests there’s a slight trend upwards. Your line might be different, but it’s unlikely to be that different.

Often, if you’re looking to forecast what’s going to happen in the near future, a straight-line extrapolation from the past is a good starting point. Here, for example, is a chart showing the proportion of all grocery spending that was done online from 2013 (2.1%) to 2017 (4.8%). Care to guess what happened in 2018?10

The online market was clearly growing each year, though not by a fixed amount. The annual growth was just 0.4% in 2014, and for the next three years it was in the range 0.6% to 0.8%. A guess of 0.7% growth seems sensible for 2017–18. Of course it might be as high as 1% or as low as 0.3%, or it might do something cataclysmic, we can’t be sure, but like steering an oil tanker, statistics that are heading steadily in one direction can take a lot of effort to shift to a different path. So a prediction of 5.5% (ish) for 2018 is a relatively safe bet – and as it happens, 5.5% is exactly what the growth was that year. But I’ve been a bit lucky here – informed guesses aren’t always as accurate as this.

The further into the future you are trying to forecast, the more risky it is to extrapolate a trend from the data you have. And be careful: while the grocery purchasing habits of the USA are clearly revealing a changing pattern of consumer behaviour, it’s possible for an ‘upward trend’ to happen purely at random. If I repeatedly toss 10 coins and get four heads the first time, five heads the second time and six heads the third, it might look like an upward trend, but the stats say that the most likely outcome next time is going to be five.

Finally, buried within a long-term trend, there might well be short periods where the data moves in the opposite direction.

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