While preparing a presentation for senior management, a data analyst wants to emphasize observations that deviate substantially from the mean. She decides to apply a statistic that squares each data point's distance from the arithmetic mean before averaging those squared values. Which metric satisfies this requirement?
The calculation that squares each distance from the average and then computes an average of those squared values is known as variance. While standard deviation is derived from variance by taking the square root, variance directly represents the average of squared deviations. Range and interquartile range measure overall spread or the spread of the middle half of the data but do not incorporate the squaring of individual deviations from the mean.
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Why is variance used instead of standard deviation to highlight large deviations?
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What does squaring the deviations achieve in variance calculations?
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How does variance differ from range or interquartile range in measuring spread?