Question: State the characteristics of the standard deviation and explain the empirical rule.

• The standard deviation is always positive, and it is used to describe quantitative data, typically reported with the mean, and affected by the value of each score in a distribution. Adding or subtracting the same constant to each score will not change the standard deviation. Multiplying or dividing each score using the same constant will cause the standard deviation to change by the constant.

• For normal distributions with any mean and any variance, we can make the following three statements using the empirical rule:

(1) At least 68% of all scores lie within one standard deviation of the mean,

(2) at least 95% of all scores lie within two standard deviations of the mean, and

(3) at least 99.7% of all scores lie within three standard deviations of the mean.