Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Prove that Pearson's second measure of Skewness that is

Skewness = 3(Mean - Median)/Standard deviation

lies between -3 and +3

share|cite|improve this question

It would be simpler to state this question as proving that the difference between the mean and the median is less than or equal to one standard deviation.

There are various proofs of this. I think the easiest is to start from the one-sided version of Chebyschev's inequality

$$\Pr(X-\mu \gt k\sigma)\lt \frac{1}{1+k^2}$$

and let $k=1$ so

$$\Pr(X \gt \mu + \sigma)\lt \frac{1}{2}$$

so the median is less than or equal to $\mu + \sigma$ (and, by reversing the sign of $X$ and $\mu$, is also greater than or equal to $\mu - \sigma$). QED

Multiply by 3 for your statement.

share|cite|improve this answer
okay thank u so much :) – linear Jun 22 '11 at 18:56

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.