This means there is a 68% probability of randomly selecting a score between -1 and +1 standard deviations from the mean.ĩ5% of the values fall within two standard deviations from the mean. The empirical rule allows researchers to calculate the probability of randomly obtaining a score from a normal distribution.Ħ8% of data falls within the first standard deviation from the mean.
If the data values in a normal distribution are converted to standard score (z-score) in a standard normal distribution the empirical rule describes the percentage of the data that fall within specific numbers of standard deviations (σ) from the mean (μ) for bell-shaped curves. The empirical rule is often referred to as the three-sigma rule or the 68-95-99.7 rule. The empirical rule in statistics allows researchers to determine the proportion of values that fall within certain distances from the mean. Probability and the normal curve: What is the empirical rule formula?
