A standard deviation can never be

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BlackTom AI · Accepted Answer

When considering what a standard deviation can or cannot be, it helps to recall its definition as a measure of spread that is always a nonnegative quantity. 
Option 1: 'negative' — This is incorrect because standard deviation is defined as the square root of a variance, and variances are nonnegative, so their square roots cannot be negative.
Option 2: 'positive' — In many practical situations, standard deviation is greater than zero, indicating some spread in the data. However, this option may be interpreted as stating it can always be positive, which isn’t universally true since zero is possible in perfectly constant data.
Option 3: 'zero' — This is a valid possibility: if all data values are identical, there is no variability, and the standard deviation is exactly zero.
Option 4: 'none' — This is not a correct feature of standard deviation, because standard deviation must be defined as a nonnegative quantity and, as noted, can be zero in the degenerate case of no variability.
Overall, the reasoning hinges on the fundamental properties of standard deviation being nonnegative and potentially zero in a fully constant dataset, while never taking a negative value.

ECON 3640-090 Summer 2025 Assignment 4: Dispersion

A standard deviation can never be

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