# Statistical trickery: Numbers aren't always what they seem

Written by lee johnson
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“Ask yourself: what is the mean number of legs possessed by human beings? Bearing in mind that, very sadly, a small number of people have a single leg, or none at all, the answer is something like 1.9999. Therefore, almost everyone has an above-average number of legs.”

Numbers have a reputation for reliability. As counter-intuitive as it might be, this is precisely the reason they’re used so often to mislead. If you hear that the average Briton owes £1,567 in credit card debt, you’re inclined to believe it because it implies that research has been conducted and they have arrived at a definitive result. Likewise, you might be shocked at the news that a company has laid off 25 percent of its entire workforce, because 25 percent is a very significant figure. These seem like incontrovertible facts, until you learn a little bit about statistics and realise that people owing £10,000 on credit cards makes up for all of those who owe nothing, and that the company’s workforce only totalled eight employees.

## Ambiguous averages

Averages are commonly banded around, but very rarely is there any discussion of what type of average they’re discussing. The mean is the one most people think of when averages are being discussed – in this case, the average test score from eleven pupils is the total cumulative score divided by eleven. But you could also take the mode, another type of average, or the median, yet another one. This should bring back memories of some early maths lessons, but when put into practice you can use it to justify some pretty spurious claims. The class who achieved an average score of just over 11.6 (mean) could also be thought to have a modal average of 18.

Consider this example from University College London philosophy professor Jonathan Wolff, “the most common number of readers for academic papers, once published, is zero.” This makes it sound as though the average academic paper will have been read by nobody, but this is one of the ways a mode can be snuck into reporting and rhetoric. Of course the most common number of readers is zero, because it’s hardly going to be 478, or 2,189, is it? The mode is simply the most commonly occurring number, so in our above example we could accurately state that the most common score for our class of eleven was 18, even though the mean was pulled down by the lower scores.

The median is a much simpler way of determining the average, because it just involves lining the results up and selecting the middle one as the average. In the test results, (3, 5, 8, 9, 10, 11, 12, 15, 18, 18 and 19) 11 is the median, which is actually pretty close to the mean. However, if the person who scored 11 actually scored 9, the median would be 10 and the mean would have been barely affected (coming to around 11.4). If the test was out of 50, the top score could have been a perfect 50 but the median would still have been 11.

## Percentages or absolute numbers? Whichever sounds better

Newspapers tend to choose the figure which has the greatest impact. If a multinational corporation lays off a measly 2 percent of its staff, that figure could be 30,000 employees. The choice between these two numbers is a choice between a number that shows the true scale of their changes in relation to the size of the company, and the other in relation to, well, nothing. The number 30,000 appears to be a very large one indeed, so media outlets with blatantly favour it over the pathetic-sounding 2 percent. The problem with numbers is that they have no frame of reference; without learning that the company has 1.5 million employees the information holds no real value.

Omitting the percentages creates problems in how the public perceives a problem. For example, you could point out that between 2006 and 2007, 63 schoolchildren were killed in America. Criminologist James Alan Fox from Northeastern University points out that, “When you consider the fact that there are over 50 million schoolchildren in America, the chances are over 1 in 2 million, not a high probability.”

As you may expect, in situations when the percentage is much more shocking, they’ll go for that instead. If a smaller company made five employees redundant, it would be much more shocking to say that 33 percent of their employees had been fired. Writing in the Journal of Philosophy, Jonathan Adler said “figures don't lie: liars figure.” If you want to make company X sound inhuman, displaying the data in the most jaw-dropping fashion is essential.

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