Suppose that a biologist states that the average height of undergraduate students at your university is 205 cm plus or minus a standard deviation of 17 cm. What does this mean?
Does it mean that the height of undergraduates at the university ranges from 17 cm less that the average and 17 cm greater than the average?
1 answer
It means that 1 sigma (1 standard deviation) or 68% of the students will fall within +/- 17 cm of 205 cm and 95% of the students will fall within 2 sigma or +/- 34 cm of 205 cm. (And 99% will fall with 3 sigma or 205 +/- 3*17 cm.