Question

explain the relationship between variance and standard deviation. can either of these measures be negative? explain. choose the correct answer below. a. the variance is the negative square root of the standard deviation. the variance can be negative but the standard deviation can never be negative. b. the standard deviation is the positive square root of the variance. the standard deviation and variance can never be negative. squared deviations can never be negative. c. the variance is the positive square root of the standard deviation. the standard deviation and variance can never be negative. squared deviations can never be negative. d. the standard deviation is the negative square root of the variance. the standard deviation can be negative but the variance can never be negative.

Explanation:

The standard deviation is defined as the positive square root of the variance. Variance is calculated as the average of the squared deviations from the mean. Since squared values are always non - negative, both variance and standard deviation are non - negative.

Answer:

B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.