Standard Deviation

Characteristics of the Standard Deviation

1. The standard deviation is always positive: SD>0. The standard deviation is a measure of variability. 2. The standard deviation is used to describe quantitative data, which are data measured in numeric units. 3. Standard deviations are typically reported with the mean. The standard deviation is the average distance that scores deviate from their mean. (99.7% of data fall within 3 SD of the mean)

Empirical Rule

The empirical rule states that for any normally distributed set of data, at least 99.7% of data lie within three standard deviations of the mean, at least 95% of data lie within two standard deviations of the mean, and at least 68% of data lie within one standard deviation of the mean.

Standard Deviation

The standard deviation, also called the root mean square deviation, is a measure of variability for the average distance that scores deviate from their mean. It is calculated by taking the square root of the variance.

Variance

The variance measures the average squared distance that scores deviate from their mean. The value of the variance can be 0 (no variability) or greater than 0 (there is variability).

The Proportion of Area within each Standard Deviation of the Mean

This is the same as saying that half (.50) of the area under the normal curve falls above and half (.50) falls below the mean. Figure 6.2 shows the proportions of area under the normal curve 3 SD above and below the mean (±3 SD).