The standard deviation can be negative for a continuous random variable.

The standard deviation can be negative for a continuous random variable.

• A. True
• B. False
• C. It can be negative under certain conditions
• D. Not enough information

Answer: (B)

The standard deviation cannot be negative. It is defined as the square root of the variance, and the variance is E[(X − μ)²], which is always greater than or equal to zero. Taking the square root of a nonnegative number yields a nonnegative result, so the standard deviation is always ≥ 0. It is zero only when there is no variability (the variable is constant). This holds for any random variable, including continuous ones. Therefore, the statement is false.

The standard deviation cannot be negative. It is defined as the square root of the variance, and the variance is E[(X − μ)²], which is always greater than or equal to zero. Taking the square root of a nonnegative number yields a nonnegative result, so the standard deviation is always ≥ 0. It is zero only when there is no variability (the variable is constant). This holds for any random variable, including continuous ones. Therefore, the statement is false.