# How do I evaluate standard deviation?

I have collected responses from 85 people on their ability to undertake certain tasks.

The responses are on a five point Likert scale:

5 = Very Good,
4 = Good,
3 = Average,
2 = Poor,
1 = Very Poor,

The mean score is 2.8 and the standard deviation is 0.54.

I understand what the mean and standard deviation stand for.

My question is: how good (or bad) is this standard deviation?

In other words, are there any guidelines that can assist in the evaluation of standard deviation.

For example, if you were testing the math skills of students in a calculus course, you could get a very small sd by asking them questions of elementary arithmetic such as $3+2$. But suppose you gave a more serious placement test for calculus (that is, students who passed would go into Calculus I, those who did not would take lower level courses first). You might expect a lower sd (and a higher average) among freshman at MIT than at South Podunk State, given the same test.