I understand how to calculate the mean, variance and standard deviation of a given set of numbers, and I also understand the standard deviation is a measure of spread from the mean.
In most texts (and blogs, and articles), we learn that a "small standard deviation" means most of the data values fall on or near the expected value and a "large standard deviation" means that there is more spread. Got it. What are the definitions of "small" and "large" in this context?
Do you take the value of the standard deviation and compare it to the mean? The median? Something else?
Here's a real-life example: I have 28 college students and I just calculated their final grades using Excel. Here are the summary statistics:
So, based on the data presented, is the standard deviation "large" or "small"? What are you comparing it to to make this determination?
Thank you, John