"Specifically, the mean of the 28 participants in the experimental condition, reported as 5.19, cannot be correct. Since all responses were integers between 1 and 7, the total of the response scores across all participants must also be an integer in the range 28–196. The two integers that give a result closest to the reported mean of 5.19 (which will typically have been subjected to rounding) are 145 and 146. However, 145 divided by 28 is 85714217.5, which conventional rounding returns as 5.18. Likewise, 146 divided by 28 is 42857121.5, which rounds to 5.21. That is, there is no combination of responses to the question that can give a mean of 5.19 when correctly rounded."
(that example is a fictional one but the same issue arises elsewhere)
