Standard Deviation and Variance

Standard deviation and variance are types of statistical properties that measure dispersion around a central tendency, most commonly the arithmetic mean. They are descriptive statistics that measure variability around a mean for continuous data. The greater the standard deviation and variance of a particular set of scores, the more spread out the observations (or data points) are around the mean.

Standard deviation and variance are closely related descriptive statistics, though standard deviation is more commonly used because it is more intuitive with respect to units of measurement; variance is reported in the squared values of units of measurement, whereas standard deviation is reported in the same units as the data. For example, to describe data on how long it took respondents to take a survey, a researcher would first determine the mean of the observations in the dataset, which would be reported in seconds. To examine the spread of the data, the researcher could calculate the variance in her data, reported in seconds squared, which are units that are not intuitive. On the other hand, a standard deviation could describe the variability around the mean, which is reported in seconds. Standard deviation is the accepted measure of spread of a normal distribution, which can be fully described using the mean and standard deviation.

In defining standard deviation and variance, this entry describes how to calculate these descriptive statistics manually and using computer software. It also describes how they are typically reported in the communication literature. In addition, it discusses standard deviation and variance as sample statistics, differentiating between biased [Page 1666]and unbiased estimators of respective population parameters.

Measures of dispersion are fundamental descriptive statistics. In particular, standard deviation is an important property of distributions of data and is integral to understanding sampling error, which is used in many statistical procedures, including inferential statistics. On a basic level, standard deviation and variance put scores into perspective. For example, knowing the mean and standard deviation on any particular exam allows students to assess how well they did relative to other students in the course.