hin-1-2-and-3-standard-deviations-is-the-empirical-rule-appropriate-here-and-why

Question

A dataset of response times shows a long right tail and median much smaller than mean. A student suggests using the empirical rule to estimate percentages within 1, 2, and 3 standard deviations. Is the empirical rule appropriate here, and why?

Accepted Answer

No — because the distribution is skewed (long right tail) and not approximately normal, so the empirical rule's approximations would be unreliable.

Answer

Yes — skewness does not affect the empirical rule as long as the mean and standard deviation are calculated correctly; the rule gives approximate percentages regardless of shape.

Answer

Yes — because the presence of a longer tail only affects extreme values, but central percentages near the mean will still follow 68–95–99.7 exactly.

Answer

No — because empirical rule can only be used when the mean equals the median; since they differ, it fails, even if the distribution were symmetric.