Central Tendency

Three measures of central tendency are commonly used in research. When a numeric description, such as a measure of central tendency, describes a sample, it is a statistic; when it describes a population, it is a parameter. The mean is the arithmetic average of the data. The median is the midpoint of the data set; 50% of scores fall on either side of the median. The mode is the most common score in the data set. When there’s one mode, the distribution is unimodal; when there are two modes, it’s bimodal; and when there are three or more modes, it’s multimodal. The mean is highly influenced by outliers, whereas the median and mode are resistant to outliers.

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Measures of Variability

The range is the simplest measure of variability to calculate. It is calculated by subtracting the minimum score in a data set from the maximum score. Variance and standard deviation are much more common measures of variability. They are used when the preferred measure of central tendency is the mean. Variance is the average of the squared deviations from the mean. It is calculated by subtracting the mean from every score to get deviations from the mean, then squaring each of the deviations. (In future chapters, we will use the sum of squares of the deviations when making inferences about a population based on a sample.) Standard deviation is the square root of variance. It is the typical amount that a score deviates from the mean.