Question

which of the following is not a property of the standard deviation? choose the correct answer below. a. the value of the standard deviation is never negative. b. when comparing variation in samples with very different means, it is good practice to compare the two sample standard deviations. c. the standard deviation is a measure of variation of all data values from the mean. d. the units of the standard deviation are the same as the units of the original data.

Explanation:

• Option A: Standard deviation is the square root of variance (which is a sum of squared deviations), so it's non - negative. This is a property.
• Option B: When comparing variation in samples with different means, we should use the coefficient of variation (standard deviation divided by mean) instead of just standard deviation. So this is NOT a property of standard deviation.
• Option C: Standard deviation measures how far data values are from the mean (it's a measure of variation), this is a property.
• Option D: Since standard deviation is calculated from the original data (in the same units, as deviations are in original units and then we take square root etc. which preserves the unit in a sense), its units are the same as original data. This is a property.

Answer:

B. When comparing variation in samples with very different means, it is good practice to compare the two sample standard deviations.