ABSTRACT
The standard deviation formula is simply the square root of the variance. It is the most commonly used measure of spread. An important attribute of the standard deviation as a measure of spread is that if the mean and standard deviation of a normal distribution are known, it is possible to compute the percentile rank associated with any given score. In a normal distribution:
• 68.27% of the data is within one standard deviation of the mean. • 95.46% of the data is within two standard deviations of the mean. • 99.73% of the data is within 3 standard deviations. • 99.99% of the data is within 4 standard deviations. • 99.99985% of the data is within 6 standard deviations (i.e., within six sigma).
