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?
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.
Yes, that is correct. When the biologist states that the average height of undergraduate students at the university is 205 cm plus or minus a standard deviation of 17 cm, it means that the height of undergraduates can vary within a range of 17 cm below to 17 cm above the average height of 205 cm. This provides a measure of the variability or spread of heights among the students at the university.
Yes, that is correct. When the biologist states that the average height of undergraduate students at your university is 205 cm plus or minus a standard deviation of 17 cm, it means that the average height is 205 cm, and the range in which the heights of the students can vary is 17 cm below the average (205 - 17 = 188 cm) and 17 cm above the average (205 + 17 = 222 cm).
So, according to the biologist's statement, you can expect most of the undergraduate students' heights to fall within the range of 188 cm to 222 cm, with some students possibly being slightly shorter or taller than that range.