Question

government agencies keep data about the income distribution of the population. the tran family and morgan family live in a county with 6000 families. the tran familys income is at the 26th percentile. the morgan familys income is at the 33rd percentile. (if necessary, consult a list of formulas.) (a) which of the following must be true about the tran familys and the morgan familys incomes? the morgan family earns $7000 more than the tran family. the tran family earns $7000 more than the morgan family. both the tran family and the morgan family earn more than the median income. both the tran family and the morgan family earn less than the median income. (b) which of the following must be true about the tran familys income?

Explanation:

Step1: Recall median and percentile concept

The median is the 50th - percentile. If a value is at the 26th percentile and another at the 33rd percentile, both are less than the 50th - percentile.

Step2: Analyze part (a)

Since the Tran family is at the 26th percentile and the Morgan family is at the 33rd percentile, and the median is the 50th percentile, both families earn less than the median income. We have no information about the actual income difference in dollars.

Step3: Analyze part (b)

The Tran family's income is at the 26th percentile. This means that 26% of the families have an income less than or equal to the Tran family's income, and 74% of the families have an income greater than the Tran family's income.

Answer:

(a) Both the Tran family and the Morgan family earn less than the median income.
(b) 26% of the 6000 families in the county have an income less than or equal to the Tran family's income, and 74% of the families have an income greater than the Tran family's income.