How to determine if Standard Deviation is high/low?

Question

I have derived the following response time data for a performance test I am running: Min - 8sec Max - 284sec Average - 28sec Standard Deviation - 27sec What does the standard deviation say about the response time data distribution? When you say low/high standard deviation, what does this actually mean? Is this in comparison to the Average/Min/Max? I know what standard deviation is and how it's computed. I'm just not sure how to tell if it is high or low.

Answer 1

I think you are probably referring to standard error. When you use a sample and don't have the entire population the standard error is an estimate of your standard deviation .

The term high or low standard deviation is relative. Your standard deviation would depend on your data size and application. I high standard deviation would mean that your data points seem to vary greatly from the mean while a low standard deviation tells you that your data points do not very greatly from the mean. To understand your data better I would calculate other summary statistics such as the median which is a better description of central tendencies since the average is more effected by outliers. You may also calculate other statistics such as the skewness ,the third central moment, which tells you how symmetrical your distribution is and the kurtosis, the fourth central moment, which tells you the tail heaviness . For example the kurtosis of a normal distribution is about 3 .

Standard deviation can also be put in better context when you know what type of distribution or approximately what type of distribution you are dealing with . For example, for a normal distribution the empirical rule states that approximately 95% of the observations fall within 2 standard deviations of the mean and approximately 99.7% of the observations fall within 3 standard deviations of the mean.

I hope this was helpful.