The Mean and Standard Deviation

This chapter describes a set of scores with only two statistics: the mean, which describes its average, and the standard deviation, used to describe its variability. The term variability refers to the amount by which participants vary or differ from each other. The standard deviation has a special relationship to the normal curve. If a distribution is normal, 68% of the participants in the distribution lie within one standard-deviation unit of the mean. When researchers calculate the standard deviation, they are actually calculating the number of points that one must go out from the mean to capture 68% of the cases. Perhaps more importantly, 95% of cases correspond to 1.96 standard deviations. The normal curve is not an invention of statisticians. Instead, it is a curve that has been observed with great frequency in nature. Statisticians derived the standard deviation in order to have a standardized method for describing the variability of normal distributions.