Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have run many trials with random data (to compare with a real set) and found that about 90% of items occur within one-third of the mean which suggests that where the size of SD approaches the mean then randomness is less likely (even for a normal distribution!). Investigations with relative mean deviation (MD/Mean) on random data sets also show that it tends to 20+% as the number of items is increased. A distribution too regular or too clumped (even about the mean) is unlikely to be a result of chance. Is there a theoretical SD to mean formulation that can express probability of randomness? Stating 68% of values occur within 1 SD does not address this. Thanks.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.