City Planners Wanted to Know How Many People Live in a Typical

Essay

City planners wanted to know how many people live in a typical housing unit so they compiled data from hundreds of forms that had been submitted in various city offices. Summary statistics are shown in the table.
$\begin{array}{|c|c|}\hline\bar{x} & 2.53 \text {people} \\\hline \text { s } & 1.40 \text {people} \\\hline\text { min } & 1 \\\hline\text { Q1 }& 1 \\\hline \text {median} & 2 \\\hline \text {Q3} & 3 \\\hline \text {max } & 10 \\\hline\end{array}$

a. Notice that the minimum occupancy and the first quartile are the same. Explain how this can be.
b. The city classifies residences housing 4 or more people as "high occupancy". Would you consider 4 occupants to be unusually high? Explain.
c. The city bases their garbage disposal fee on the occupancy level of the home or apartment. The annual fee is $40 plus $5 per person, so a single occupant pays $45 and the homes with 10 people pay $40 +$5(10) = $90 a year. What is the median fee paid? And the IQR?
d. What are the mean and standard deviation of the garbage disposal fees?