# A Dicey Survey

## If you want to test MPs' stats skills, ask the right questions.

The Royal Statistical Society recently did a survey to test out the statistical skills of Britain's Members of Parliament.  Great idea - it's vital that our politicians have a good grasp of the statistics they have to deal with every day.

The survey conclusion was that while the politicians performed better in the test than they did ten years ago, there is still room for improvement.

But I'm concerned that the survey itself was flawed, particularly the questions about dice scores.

The dice questions were these:

If you roll a six-sided dice* and the rolls are 1, 3, 1, 4 and 6 then

(a) what is the mean score, and

(b) what is the mode?

64% of MPs correctly answered '3' for the mean, and 63% correctly said '1' for the mode.  What does this tell us about their stats skills?  In my view: not much.

Mean score

The problem with the question about the mean is that it's quite likely that many MPs guessed the right answer but using the wrong logic. In that list of five dice rolls, 3 is the middle (median) value, so any MP interpreting 'mean' as 'median' would answer 3.  And there's a second way in which they might end up answering 3 with fallacious reasoning. Maybe they just thought that 3 is the average score you get when you roll a dice. I asked two quite numerate adults what the average score is when you roll a dice, and both of them answered 3.  Why? Because that feels like it's the middle number between 1 and 6.  The correct answer is 3.5, of course!  So I expect that many MPs gave the right answer for the wrong reason. The researchers would have been better posing a question where the mean was (say) 2.5 or 4.

Mode score

Is this a stats question, or a language question?  Although the word mode is drilled into us at school, most people soon forget what it means, and it is generally regarded as mathematical jargon.  When the word mode is used in public broadcasting, it is then usually explained in layman’s terms.  “What is the mode, i.e. what is the most common value?”.  If the MPs had been asked “which value appears most often in this list?”, surely all but the most obtuse of them would have answered ‘1’.

So in conclusion: yes, MPs could do better.  But so could the researchers.

* I'm using the word dice to mean a singular die, as most people do these days.