This is a big source of confusion when it comes to errors. I think most people think intuitively in terms of a 'peak-to-peak' specification of errors, i.e. rang

This is a big source of confusion when it comes to errors. I think most people think intuitively in terms of a 'peak-to-peak' specification of errors, i.e. range of X means that all possible values are within that range. But that's not really how statisticians think, and they tend to think in terms of standard deviation. Even if you soften the 'intuitive' view to 95% confidence range, that's about a 6x difference in terms of what the number means (assuming, optimistically, a gaussian distribution).