Diversity Index Shannon’s diversity index is a measure of the diversity of a population. The diversity index is given by the formula

where p₁ is the proportion of the population that is species 1, p₂ is the proportion of the population that is species 2, and so on. In this problem, the population is people in the United States and the species is race.

(a) According to the U.S. Census Bureau, the distribution of race in the United States in 2021 was: Compute the diversity index of the United States in 2021.

(b) The largest value of the diversity index is given by H_max = log(S), where S is the number of categories of race. Compute H_max.

(c) The evenness ratio is given by E_H= H/H_max, where 0 ≤ E_H ≤ 1. If E_H = 1, there is complete evenness. Compute the evenness ratio for the United States.

(d) Obtain the distribution of race for the United States in 2010 and 2020 from the Census Bureau. Compute Shannon’s diversity index. Is the United States becoming more diverse? Why?

Transcribed Image Text:

H = -(pilog p₁ + P2 logp2 + + Pn log Pn)