Q R1.8. - The Practice of Statistics for AP

Question

Household incomes Rich and poor households differ in ways that go beyond income. Following are histograms that compare the distributions of household size (number of people) for low-income and high-income households.$53$ Low-income households had annual incomes less than $\backslash (15,000$ and high-income households had annual incomes of at least $\backslash )100,000$

(a) About what percent of each group of households consisted of two people?

(b) What are the important differences between these two distributions? What do you think explains these differences?

Step-by-Step Solution

Answer

Part (a) About $20\%$ of low income group household consists of $2$ people and about $34\%$ of high income household consists of $2$ people.

Part (b) Low-income households have a strongly positive skewed distribution, while high-income households have a modestly positive skewed distribution.

Part (a) Step 1: Given information

Part (a) Step 2: Concept

Data Analysis, Statistics, and Probability introduces statistics as a problem-solving process.

Part (a) Step 3: Explanation

About $20\%$ of low-income households are made up of two persons, while $34\%$ of high-income households are made up of two people.

Part (b) Step 1: Explanation

Low-income families have a strictly positive skewed distribution, while high-income households have a somewhat positive skewed distribution. A household with a single person is quite likely to fall into the low-income category, with an income of less than $\$15000$; the high-income category includes households with an income of at least $\$10000$, which will presumably have fewer people due to criteria such as education status.