We are in the midst of an intense election season here in the United States and it seems that some politicians will say anything in order to get votes. This should come as no surprise. As my father used to tell me the one most important qualification needed to be a successful politician is to be an artful lier. One of the most efficient tactics used by politicians as well as companies and public officials to mislead is statistics. As British Prime Minister Benjamin Disraeli said: “There are three kinds of lies: lies, damned lies, and statistics.”
This does not mean that statistics are lies. It means that statistics are often used as an elegant way to mislead without having to outright lie. In order not to be fooled it is important to understand how this is done. One of the most effective way of lying with statistics is to cherry pick the statistic that agrees with one’s point and ignore those that do not. Politicians do this the whole time and most people do not notice.
One of the most common ways of misleading by cherry picking statistics is by reporting only one measure of central tendency and leaving out the rest that do not support the given argument. There are overall three measures of central tendency: the mean (also known as the average), the median and the mode. To get a full understanding of what is going on in any data, it is important to know all three. But most often we only hear about the mean or the median but not both. This is often because reporting both would be inconvenient for the point being made.
I have created an interactive app that will explain this more clearly and intuitively, using the example of a group of people’s incomes. The app will allow you to play with the numbers and see clearly, on your own, how leaving one indicator of central tendency out can easily mislead. See that app here.
There is another element of a data set that also should be reported and that is how the data varies, known as the variance and/or the standard deviation. Leaving that out can also seriously mislead. That will be the topic of my next post. But to understand that it’s important to understand central tendency first. See the central tendency app here.