Much of the "error analysis" actually done (using standard deviations) by students in biology, chemistry, social science, and physics courses is improperly done, and is so much garbage. Reason: No one's brain was engaged. It had become a "by the rules" unthinking automated process. And I go further. Some of the published research papers are similarly flawed, because somewhere along the line the researchers received an inadequate education in this subject. Books on statistical treatment of errors usually discuss this thoroughly, but those summaries you find in the front of undergraduate lab manuals don't warn you about the limitations of the formulae they present, placing great emphasis on the "bottom line" equations. So students have this silly notion that if you don't use standard deviations in every case, it isn't "professional".