Question

Excel is used to find the mean and standard deviation of a discrete probability distribution and the results are asâ follows: mu equals 2.0 and sigma equals negative 3.5 . Can these results beâ correct? Explain. Choose the correct answer below. A. No. The mean must be negative if the standard deviation is negative. B. No. The standard deviation cannot be negative. C. Yes. The results can be correct. D. No. The standard deviation is too large.

Answer 1

Option B) No. The standard deviation cannot be negative.

Explanation:

We are given the following in the question:

`\mu = 2.0\\\sigma = -3.5`

The above results are not possible.

• The mean of data can be positive or negative
• The standard deviation of data can never be negative.
• Standard deviation is defined as the square root of squares of difference from the mean divide by the number of observations.
• It tells us about variation of data.
• The standard deviation may be smaller or greater than the mean but it cannot have a negative value.
• Thus, the correct answer is

Option B) No. The standard deviation cannot be negative.