Empirical Rule Calculator

Empirical Rule Calculator calculates three different distribution range by given mean and standard deviation.

Empirical Rule Formula

The empirical rule formula is

68% of data falls: μ-σ to μ+σ
95% of data falls: μ-2σ to μ+2σ
99.7% of data falls: μ-3σ to μ+3σ

while μ = mean
σ = Standard Deviation

For example, if there is a data set of test scores which normally distributed, the mean for the scores is 60, and the standard deviation is 12.
based on the empirical rule formula.

60-12=48 and 60+12=72
60-12x2=36 and 60+12x2=84
60-12x3=24 and 60+12x3=96

Therefore
68% of students have test scores between 48 to 72
95% of students have test scores between 36 to 84
99.7% of students have test scores between 24 to 96