Confidence Intervals
The fact that the standard deviation measures the degree of variation without regard for the direction is not a problem in symmetrical distributions.
However, if the distribution is not symmetrical, there may be a significantly greater chance of a variation in one direction rather than the other.
Another way of establishing confidence for a probability distribution is to estimate confidence intervals directly, using a statistical sampling. Establishing a confidence interval directly means determining a pair of values within which we have some confidence that the outcome will fall. The interval needs to be qualified by the degree of confidence required.
For example, a 90% confidence interval would be a pair of values between which the outcome in question has a 90% chance of falling.
It is normally implicit that the interval should be symmetrical, in the sense that there would be an equal probability that the outcome would fall outside the confidence interval in either direction.
Because the distribution itself may be skewed, this means that the confidence interval is not, in general, symmetrically placed with respect to the mean value.
In general, confidence intervals calculated in this manner are to be preferred to those based on standard deviations because the skew in the underlying distribution is indicated.
In some cases, however, standard deviations are more reliable indicators of confidence. This is particularly true for relatively small samples because standard deviations are based on all outcomes instead of a few extreme values.
Example
In the random selection of any number between 1 and 100, there is a 90% confidence interval that the number chosen will be greater than 5 and less than 96.