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 17cm. What does this mean?
That about 68% of undergrad students fall between 205±17cm and about 95% fall between 205±34 cm.
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 they have calculated the average height to be 205 cm, and they believe that the actual heights of the students will mostly fall within a range of 17 cm above or below that average.
To understand this statement more clearly, we need to consider the concept of the standard deviation. The standard deviation is a measure of how spread out the data points are from the mean (average). In this case, the standard deviation is given as 17 cm.
So, based on this information, we can infer that the biologist is confident that most of the undergraduate students' heights at your university will fall within the range of 188 cm to 222 cm. However, there will still be some students whose height will fall outside this range, but they will be relatively uncommon.
In summary, when the biologist states the average height as 205 cm plus or minus a standard deviation of 17 cm, it indicates the expected range within which the majority of the students' heights are likely to fall.