What does the variance of a data set represent?
Correct Answer
C) The square of the standard deviation of that data
Why this is correct: The original explanation defines variance as "the mean of the squared deviations" and notes that standard deviation is its square root. Therefore, variance is literally the square of the standard deviation. Why the other choices are wrong: The standard deviation expressed as a percentage describes the coefficient of variation. The difference between the highest and lowest value is the range. The middle observation once the data is ordered is the median. Exam tip: Variance = (Standard Deviation)². It's in squared units (e.g., dollars²), so it's hard to interpret directly.
Why This Is the Correct Answer
Why this is correct: The original explanation defines variance as "the mean of the squared deviations" and notes that standard deviation is its square root. Therefore, variance is literally the square of the standard deviation. Why the other choices are wrong: The standard deviation expressed as a percentage describes the coefficient of variation. The difference between the highest and lowest value is the range. The middle observation once the data is ordered is the median. Exam tip: Variance = (Standard Deviation)². It's in squared units (e.g., dollars²), so it's hard to interpret directly.
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