Three measures of central tendency are commonly used in research. (This may be a good moment to prod your memory by looking at Table 4-1 again.) 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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The range is the simplest measure of variability to calculate. It is calculated by subtracting the minimum score in our 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 using samples to make inferences about a population.) Standard deviation is the square root of variance. It is the typical amount that a score deviates from the mean.
When the median is the preferred measure of central tendency, the interquartile range (IQR) is used, as it provides a better measure of variability than does the range. The IQR is the third quartile, or 75th percentile, minus the first quartile, or 25th percentile. The IQR is the width of the middle 50% of the data set and, unlike the range, is resistant to outliers.