Question

government agencies keep data about the income distribution of the population. the young family and collins family live in a county with 5000 families. the young familys income is at the 36th percentile. the collins familys income is at the 19th percentile. (a) which of the following must be true about the young familys and the collins familys incomes? ○ the young family earns $17,000 more than the collins family. ○ the collins family earns $17,000 more than the young family. ○ both the young family and the collins family earn more than the median income. ○ both the young family and the collins family earn less than the median income. (b) which of the following must be true about the young familys income? ○ the young family earns about 36% of the highest income in their county. ○ the young familys income is in the top half of incomes in their county. ○ the young family earns $36,000. ○ the young family earns less than about 64% of families in their county.

Explanation:

Step1: Understand percentile concept

Percentile \( p \) means \( p\% \) of the data is less than or equal to that value. For the Young family at \( 36^{th} \) percentile, \( 36\% \) of families have income \( \leq \) Young family's income. For the Collins family at \( 19^{th} \) percentile, \( 19\% \) of families have income \( \leq \) Collins family's income. So the Young family earns more than the Collins family.

Step2: Analyze median relation

Median is the \( 50^{th} \) percentile. Since Young family (\( 36^{th} \) percentile) and Collins family (\( 19^{th} \) percentile) are both below \( 50^{th} \) percentile, both earn less than the median income.

Answer:

(a) The Young family earns \( \$17,000 \) more than the Collins family. (b) Both the Young family and the Collins family earn less than the median income.