Questions: Which of the following is NOT a property of the standard deviation? Choose the correct answer below. A. The standard deviation is a measure of variation of all data values from the mean. B. The value of the standard deviation is never negative. C. When comparing variation in samples with very different means, it is good practice to compare the two sample standard deviations. D. The units of the standard deviation are the same as the units of the original data.

Solution Steps

To determine which statement is NOT a property of the standard deviation, we need to evaluate each option based on the known properties of standard deviation. The standard deviation is a measure of how spread out numbers are in a data set. It is always non-negative, has the same units as the data, and is used to measure variation from the mean. However, comparing standard deviations directly when the means are very different is not always appropriate, as it doesn't account for relative variation.

The standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. It has several key properties:

• It measures the variation of all data values from the mean.
• It is always non-negative, as it is derived from the square root of the variance.
• It has the same units as the original data.

Let's evaluate each statement to determine which one is NOT a property of the standard deviation:

• Statement A: This is true. The standard deviation measures how much the data values deviate from the mean.
• Statement B: This is true. The standard deviation cannot be negative.
• Statement C: This is false. When comparing samples with very different means, it is not always appropriate to compare their standard deviations directly, as it does not account for relative variation.
• Statement D: This is true. The units of the standard deviation are the same as those of the original data.

Final Answer