Let's analyze the given percentages of social networking site usage in different cities and determine which city would be the best cluster to use for a survey. This will be done by finding which city's percentage is closest to the overall 28% usage in the United States.
Here's the data provided:
- Denver: 16%
- Honolulu: 9%
- Miami: 27%
- Philadelphia: 46%
We start by calculating the absolute difference between the percentage of each city and the overall 28% for the United States.
1. Denver:
- Percentage of usage: 16%
- Difference from 28%: [tex]\( |16\% - 28\%| = | -12\% | = 12\% \)[/tex]
2. Honolulu:
- Percentage of usage: 9%
- Difference from 28%: [tex]\( |9\% - 28\%| = | -19\% | = 19\% \)[/tex]
3. Miami:
- Percentage of usage: 27%
- Difference from 28%: [tex]\( |27\% - 28\%| = | -1\% | = 1\% \)[/tex]
4. Philadelphia:
- Percentage of usage: 46%
- Difference from 28%: [tex]\( |46\% - 28\%| = | 18\% | = 18\% \)[/tex]
Now we compare the differences calculated:
- Denver: 12%
- Honolulu: 19%
- Miami: 1%
- Philadelphia: 18%
The city with the smallest difference from the overall percentage (28%) is Miami, with a difference of just 1%.
Thus, the best city to choose as a cluster for the survey to most closely represent the 28% usage in the United States is:
D. Miami
