Which parameter is σX?

Which parameter is σX?

• A. Location parameter
• B. Dispersion parameter
• C. Shape parameter
• D. Scale parameter

Answer: (B)

The main concept here is that σX represents the spread of the distribution of X. The standard deviation quantifies how far typical observations of X diverge from the mean, which is a direct measure of dispersion or variability. It does not tell you where the distribution is centered—that would be a location parameter. It also doesn’t describe the shape, such as skewness or peakedness, which are about the distribution’s form. While scale relates to the overall size of the distribution, σX specifically captures how spread out the values are, making it the dispersion parameter.

The main concept here is that σX represents the spread of the distribution of X. The standard deviation quantifies how far typical observations of X diverge from the mean, which is a direct measure of dispersion or variability. It does not tell you where the distribution is centered—that would be a location parameter. It also doesn’t describe the shape, such as skewness or peakedness, which are about the distribution’s form. While scale relates to the overall size of the distribution, σX specifically captures how spread out the values are, making it the dispersion parameter.