I know empirical rule and use it for a normal distribution data. I know percentile and i use it too and love it. But are there any other statistical models? Or what model gives the most accurate results? I mean is there something better than other or all of them are the best for their categories?

Hope i could explain


No, the Empirical Rule does not apply to all distributions. It is only for bell-shaped, continuous, symmetrical data.

However, Chebychev postulates a similar concept for any continuous distribution. Here is a link to Chebychev's Theorem and its relation to the Empirical Rule. According to the article,

For any numerical dataset, at least $1−\frac{1}{k^2}$ of the data lie within $k$ standard deviations of the mean, that is, in the interval with endpoints $x \pm ks$ for samples and with endpoints $\mu \pm k \sigma$ for populations, where $k$ is any positive whole number that is greater than $1$. ... It is important to pay careful attention to the words “at least” at the beginning of each of the three parts of Chebyshev’s Theorem. The theorem gives the minimum proportion of the data which must lie within a given number of standard deviations of the mean; the true proportions found within the indicated regions could be greater than what the theorem guarantees.

  • $\begingroup$ i am not very familiar with equations. What is k in this case? I mean how can we apply this rule to a dataframe? $\endgroup$ – Don Coder Aug 1 '18 at 13:33
  • $\begingroup$ @ERT +1 when k is near 2 the rule works (more or less) fairly well for a wide range of unimodal continuous densities, including ones some way from symmetry. $\endgroup$ – Glen_b -Reinstate Monica Aug 2 '18 at 13:20

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