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.

**Answer**

Standard deviations aren’t “good” or “bad”. They are indicators of how spread out your data is. Sometimes, in ratings scales, we want wide spread because it indicates that our questions/ratings cover the range of the group we are rating. Other times, we want a small sd because we want everyone to be “high”.

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.

So. What is the purpose of your test? Who are in the sample?

**Attribution***Source : Link , Question Author : Amarald , Answer Author : Peter Flom*