Can the variance of a data set ever be negative? Explain. Can the variance ever

Question

Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain. Choose the correct answer below The variance of a data set cannot be negative because deviation from the mean is always a positive value. Variance cannot be smaller than the standard deviation because the variance is the square of the standard deviation. The variance of a data set can be negative if the mean is negative. Variance can be smaller than the standard deviation if the variance is less than 0 The variance of a data set cannot be negative because it is the sum of the squared deviations divided by a positive value. Variance can be smaller than the standard deviation if the variance is less than 1. The variance of a data set can be negative if all of the data value are negative. Variance cannot be smaller than the standard deviation because the standard deviation is the squareroot of the variance.

Explanation / Answer

Answer: C

That is, the variance of the data set cannot be negative because the sum of sqaured values from the mean divided by the positive number and the variance is smaller than the standard deviation when the variance is less than 1.

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