What does the number that we get from a standard deviation formula show us?

Question

How should we describe this number?

Answer 1

It is meant to give you an idea of how dispersed your data are. If the difference between the mean and the SD is small, then your data (and hence your predictions about new data) is tightly clustered. In other words, the normal curve is tall and thin. On the other hand, a large difference between mean and SD means that you have a greater variation on your data: the normal curve is lower and wider.

Suppose you were manufacturing light bulbs, and you had a very tight SD (tall and thin normal curve) measuring how long the bulbs lasted before burn out; you could say with honesty "The bulb you buy will last 5 years" and be confident that very few bulbs would burn out sooner, nor would many last longer.

Suppose, however, that you had a wide difference between mean and SD; now you can't say the same thing with the same level of confidence.

Make sense?

HTH

Charles

Answer 2

It is the probability that any point on the distribution curve will fall on either side of the mean. Therefore, if x is the mean and s is one standard deviation than there will be a 68% probability that a number on the distribution curve will fall within x + s and x - s.