# Just Half of Politicians Can Correctly Answer This Basic Statistics Question

It may or may not surprise you to learn that only about half of UK MPs can correctly answer a basic probability question. That figure, believe it or not, is actually higher than when legislators were asked the same question ten years ago. The findings come from a new poll by the Royal Statistical Society, which questioned 101 members of parliament (MPs) in the United Kingdom a simple statistics question: what is the likelihood of getting two heads if you toss a coin twice?

One coin flip has a 50% probability of landing on heads. Because two throws are independent events, you must compound the two probabilities: 50 percent times 50 percent, giving you a result of 25%. However, only 52% of MPs who were polled gave the correct response, with the remaining 32% providing the inaccurate answer of 50%.

Politicians who had been in office for longer were more likely to deliver the correct response than those who had been elected lately. Between 2001 and 2009, up to 68 percent of MPs who took office gave the correct answer, compared to 38 percent of MPs elected in 2019. Despite what a first glance at the headlines might suggest, things have actually improved over the last decade. In a comparable poll conducted in 2011, 97 MPs were asked the same question, and only 40% of them correctly answered.

Another statistical question was posed of politicians in the most recent 2021/2022 poll: you roll a six-sided die, and the rolls are 1,3,4,1 and 6. What are the values for the mean and mode? Only 64 percent correctly identified the mean value as three, and only 63 percent correctly identified the mode as one. A third question assessed their statistical expertise, which they could readily apply to the COVID-19 epidemic (which they’ve been in responsible of for the past two years).

Consider the following scenario: suppose there was a virus diagnostic test. The false-positive rate (the number of persons who test positive even though they don’t have the virus) is one in 1,000. You took the test and got a positive result. What is the likelihood that you are infected with the virus? You’ll need three pieces of crucial information to answer this question correctly: the false-positive rate, false-negative rate, and viral prevalence, yet the question only offered one of these figures.

Only 16% of legislators correctly answered, “There isn’t enough information to know.” “Statistical skills are essential for effective decision-making and scrutiny.” While we’re pleased to see that MPs’ statistical knowledge appears to have improved, the survey results show that more needs to be done to ensure our elected representatives have the statistical skills required for their jobs,” said Stian Westlake, Chief Executive of the Royal Statistical Society, in a statement.