The distribution of income for Danville is as follows: Number of Families Income
500 less than $15,000
600 between $15,000 and $20,000
1,000 between $20,000 and $25,000
700 between $25,000 and $30,000
500 over $30,000
If the poverty rate in Danville is 33.3 percent, what is the poverty line in Danville?

Question

The distribution of income for Danville is as follows: Number of Families Income
  500 less than $15,000
600 between $15,000 and $20,000
1,000 between $20,000 and $25,000
700 between $25,000 and $30,000
500 over $30,000
 If the poverty rate in Danville is 33.3 percent, what is the poverty line in Danville?

Quizplus · Accepted Answer

The poverty rate is the percentage of families with income less than or equal to the poverty line. To find the poverty line, we need to find the income level at which 33.3% of families or less have income below it. The cumulative percentage for families with income less than or equal to $20,000 is:
(11+600)/2811 = 0.236
This means that 23.6% of families have income less than or equal to $20,000. To include an additional 9.7% of families (33.3% - 23.6%), we need to increase the income level until 9.7% of families have income below it. The cumulative percentage for families with income less than or equal to $25,000 is:
(11+600+1000)/2811 = 0.662
This means that 66.2% of families have income less than or equal to $25,000. Since we need to include an additional 9.7%, the poverty line should be slightly above $25,000. The next income level is $30,000 and 77.1% of families have income less than or equal to it, which includes 33.3% of families. Therefore, the poverty line in Danville is $20,000 to $30,000, and the best choice is B.

The Distribution of Income for Danville Is as Follows: Number