Problem $10-28($Algo$)$

Some citizens complained to city council members that there should be equal protection under the law against the occurrence of crimes. The citizens argued that this equal protection should be interpreted as indicating that high$-$crime areas should have more police protection than low$-$crime areas. Therefore, police patrols and other methods for preventing crime $($such as street lighting or cleaning up abandoned areas and buildings$)$ should be used proportionately to crime occurrence.

The city has been broken down into $20$ geographic areas, each containing $5,000$ residences. The police recognize that not all crimes and offenses are reported: people do not want to become involved, consider the offenses too small to report, are too embarrassed to make a police report, or do not take the time, among other reasons. Every month, because of this, the police are contacting by phone a random sample of $800$ of the $5,000$ residences for data on crime. $($Respondents are guaranteed anonymity.$)$ The $800$ sampled from each area showed the following incidence of crime during the past month:

$$