Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which measure describes both central tendency and dispersion?

Mean
Median
Standard Deviation
Mode

The correct answer is: Standard Deviation

The measure that describes both central tendency and dispersion is the standard deviation. Central tendency refers to a statistic that represents the center or typical value of a dataset, while dispersion indicates the spread or variation within that dataset. Standard deviation is a crucial measure for understanding how data points are distributed around the mean. It quantifies the amount of variation or dispersion from the average. A smaller standard deviation implies that the data points tend to be closer to the mean, whereas a larger standard deviation indicates that the data points are spread out over a wider range of values. In contrast, mean, median, and mode are measures of central tendency. The mean is the arithmetic average, the median is the middle value of an ordered dataset, and the mode is the most frequently occurring value. While these measures provide valuable information about the center of the data, they do not incorporate details about how spread out the numbers are, thus lacking the element of dispersion in their descriptions. Standard deviation, however, combines both aspects, making it a comprehensive measure for understanding data distribution.