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

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It may or may not surprise you to hear that just over 50 percent of politicians in the UK can answer a basic probability question correctly. Believe it or not, that figure is actually up from when politicians were asked the same question 10 years ago.

The results come from a new survey by the Royal Statistical Society that asked 101 members of parliament (MPs) in the UK a relatively simple statistics question: if you toss a coin twice, what is the probability of getting two heads?

The chance of getting heads on one coin toss is 50 percent. Since two tosses are independent events, you should multiply the two probabilities: 50 percent times 50 percent, which gives you the answer of 25 percent.

However, just 52 percent of surveyed MPs gave the correct answer, with around 32 percent giving the incorrect answer of 50 percent.

Interestingly, politicians who have been in power for longer were more likely to provide the right answer than those recently elected. Up to 68 percent of MPs who started in office between 2001 and 2009 gave the correct answer, compared to 38 percent of MPs elected in 2019.

Although a skim through the news may suggest otherwise, things have actually improved over the past decade. A similar survey carried out in 2011 asked 97 MPs the same question and just 40 percent of MPs gave the correct answer.

For the latest 2021/2022 survey, politicians were also asked another statistics question: you roll a six-sided die, and the rolls are 1,3,4,1 and 6. What are the mean and mode values? Just 64 percent were able to identify that the mean value was three and 63 percent knew the mode was one.

A third question tested their knowledge about statistics that could be easily applied to the COVID-19 pandemic (that thing they’ve been in charge of sorting out for two years). The question went as follows: suppose there was a diagnostic test for a virus. The false-positive rate (the proportion of people without the virus who get a positive result) is one in 1,000. You have taken the test and tested positive. What is the probability that you have the virus?

To answer this question correctly, you need to have three pieces of key information: the false-positive rate, the false-negative rate, and viral prevalence, yet the question only provided one of these statistics. Just 16 percent of the politicians gave the correct answer of “Not enough information to know.”

“Statistical skills are vital for good decision-making and effective scrutiny. While we’re pleased to see that it looks like MPs’ knowledge in this area has improved, the survey results highlight that more needs to be done to ensure our elected representatives have the statistical skills needed for the job,” Stian Westlake, Chief Executive of the Royal Statistical Society, said in a statement.

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Humans
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