Chapter 2: Income Standards, Inequality, and Poverty
Density
Figure 2.1: Probability Density Function
fx
x1
xMo
xM b ′ b ″ Income
xN
distribution x. Hence, 50 percent of the area underneath fx lies to the right of xM, and the remaining 50 percent lies to the left of xM. • The mode is the income in the distribution that corresponds to the largest density (locally). In figure 2.1, the distribution’s mode is denoted by xMo. Commonly, income distributions have one mode, but there can be distributions with more than one mode. A density with two modes is called bimodal and that with many modes is called multimodal. When there is more than one mode, a society is understood to be polarized in different groups according to their achievements. A polarized society may produce social tensions among different groups, which increases the chance of social unrest. These issues are discussed in more detail in chapter 3. In addition, a density function can be a useful tool for understanding the skewness of an income distribution. Skewness is a measure of asymmetry in the distribution of incomes. It arises when most incomes lie on any one side of the mean of the distribution. If more observations are located to the left of the distribution’s mean, then the distribution is positively skewed. If more observations lie to the right of the mean, then the distribution is negatively
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