What are the three ways to describe measures of spread?

What are the three ways to describe measures of spread?

• A. Variance, standard deviation, and standard error.
• B. Mean, median, mode.
• C. Range, min, max.
• D. Skewness, kurtosis, entropy.

Answer: (A)

Spread is described by how far observations lie from the center and by how precise our estimate of that center is. Variance tells us how far data points deviate from the mean on average, by averaging the squared deviations. Standard deviation is the square root of variance, so it expresses dispersion in the same units as the data and is often easier to interpret. The standard error describes how much the sample mean would vary if we repeated the study many times; it equals the standard deviation divided by the square root of the sample size, so it shrinks as n grows and reflects the precision of the mean estimate. Together, these capture both how spread the data are and how precisely we know the mean. The other options mix central tendency (mean, median, mode), range endpoints (min, max), or distribution shape (skewness, kurtosis) rather than this specific trio of spread and precision measures.

Spread is described by how far observations lie from the center and by how precise our estimate of that center is. Variance tells us how far data points deviate from the mean on average, by averaging the squared deviations. Standard deviation is the square root of variance, so it expresses dispersion in the same units as the data and is often easier to interpret. The standard error describes how much the sample mean would vary if we repeated the study many times; it equals the standard deviation divided by the square root of the sample size, so it shrinks as n grows and reflects the precision of the mean estimate. Together, these capture both how spread the data are and how precisely we know the mean. The other options mix central tendency (mean, median, mode), range endpoints (min, max), or distribution shape (skewness, kurtosis) rather than this specific trio of spread and precision measures.