Richard Warr (10/26/2011)
Interestingly there are now 39% incorrect answers but only 31% of people picked the wrong answer. I'm assuming that means that 8% chose less than three answers.
The missing wrong answers are now down to 7% (31% picked the wrong answer, 38% of answers were incorrect).
There are all sorts of possibilities. 😀
Currently the percentages of answers add up to 286%. If everyone had picked 3 answers, they would add up to 300%. So there's a 14% discrepancy. It could be that 14% of people picked only 2 answers (and half of those people had the wrong answer as one of their two), while everyone else picked 3 answers. Or perhaps 7% of people picked only 1 answer, none of those people picked the wrong answer, and everyone else picked 3 answers. Or anything in between that adds up right.
At first site that looks as if the proportion of people selecting fewer than 3 answers must be between 7% and 14%, but that's not correct: we also have to consider what might have happened if some people picked 4 answers, don't we? :w00t:
Suppose 12% of people picked 4 answers and 26% picked 2 answers (to get the 14% totals discrepancy); then no one who picked 3 answers picked the wrong answer, while 19/26 (19% of all people) of the people with only two answers picked the wrong answer.
So all we can say is that the number of people who didn't pick three answers (ie the number who picked 1,2, or 4 answers) is somewhere between 7% and 38%, while the number who picked fewer than 3 answers is somewhere between 7% and 26%.
As you can see, trying to count the proportion of people with other than 3 answers from the information provided is not very sensible, even if one uses the totals discrepancy as well as the wrong to incorrect discrepancy to limit the possibilities. 😉