Which of the following statements is true about standard deviation

Asked by wiki @ in Advanced Placement (AP) viewed by 503 People

Which of the following statements about standard deviation is true?

A. Standard deviation is always a non-negative number.
B. Standard deviation is resistant to outliers.
C. Standard deviation measures the typical distance data points in a distribution are from the median.
D. Regardless of what units the data are in, standard deviation has no units.
E. If the data is measured in hours, standard deviation would be measured in hours squared.

Answered by wiki @


Answer:

A. Standard deviation is always a non-negative number.

Explanation:

The true statement about standard deviation is that, standard deviation is always a non-negative number.

A standard deviation is calculated by taking the square root of variance and as such the value of standard deviation is always a positive number and not a negative number.

Additionally, the variance of a sample population is calculated by the summation of all the squared distances obtained from the mean divided by the total number of samples. Hence, all the values of the variance are always positive (non-negative) numbers because they are squared. Consequently, the standard deviation would as well always be a non-negative number.


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