Final answer:
A stem-and-leaf plot is used to illustrate the distribution of a data set by dividing each value into a stem and leaf. The share of total income for each quintile is calculated by summing the incomes within each quintile and then comparing with the distribution benchmarks.
Step-by-step explanation:
When creating a stem-and-leaf plot (or stemplot), we divide each data observation into a stem and a leaf. The stem is composed of all but the last digit, while the leaf is the last significant digit. For example, if you have the number 55,000, the stem would be 550 and the leaf would be 0. All leaves for a particular stem are listed in increasing order next to it. This provides a clear version of the data that is similar to a histogram, showing the distribution of the data set. The frequency of leaves on each stem can show us where most of the data values lie.
If we apply this technique to the given incomes: $55,000, $30,000, $15,000, $20,000, $35,000, $80,000, $40,000, $45,000, $30,000, and $50,000, we can see how incomes are distributed among the group. To calculate the share of total income for each quintile, we first need to order the data from smallest to largest, then divide the group into five equal parts and sum the incomes in each quintile. The comparison with the U.S. income distribution involves comparing these shares with the known shares of the U.S. distribution for the relevant year.