Key Concepts

The key concepts and terms of this chapter, with brief explanations, are:

• Dispersion — the extent to which the values of a distribution differ from their average; a measure of dispersion improves our understanding of the behaviour of an economic variable beyond what an average alone reveals.
• Range (R) — the difference between the largest and smallest values, $R = L - S$; the simplest measure, but unduly affected by extreme values and not based on all values.
• Quartile Deviation (Q.D.) — half the inter-quartile range, $\dfrac{Q_3 - Q_1}{2}$; based on the middle 50% of values and therefore not affected by extreme values; also called the semi-inter-quartile range.
• Mean Deviation (M.D.) — the arithmetic mean of the absolute deviations of the values from their mean or median; based on all values but ignores the signs of the deviations.
• Standard Deviation ($\sigma$) — the positive square root of the mean of the squared deviations from the mean; the most widely used measure of dispersion, based on all values, independent of origin but not of scale.
• Variance — the mean of the squared deviations from the mean; standard deviation is its positive square root.
• Absolute measure of dispersion — a measure expressed in the same units as the original data (range, Q.D., M.D., S.D.).
• Relative measure of dispersion — a unit-free ratio derived from an absolute measure (coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, and coefficient of variation), allowing comparison across distributions with different units or averages. …