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

A. 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.

Step-by-step explanation:

As we know that

The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation

In mathematically

[tex]\sigma = \sqrt{variance}[/tex]

And,

[tex]variance = \sigma^2[/tex]

Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive

Hence, the correct option is a.