I have a goal of estimating how many public playgrounds exist in the United States.
There are many methods of gathering real data about playgrounds, but, unfortunately, there is no single authority that can answer this question or provide a comprehensive list.
Contacting every city in the nation would be too prohibitive, and other options such as working with regional park & rec departments have proven to show how little information those departments have. (Edit: I should also note that parks != playgrounds, but playgrounds may be contained inside parks).
This problem is akin to the old interview question: How many gas stations are there in Los Angeles?
How would one go about constructing a valid estimate on the total number of public playgrounds in the United States, with a margin of error <= 5%?
Can the community think of such a methodology that is purely grounded in math?
If you propose a solution, can you calculate what your result is for comparison with the others?
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$\begingroup$If you really want 5% error bounds, you will have to survey a bunch of cities. The interview question generally accepts more like a factor of 2 to 5, even factor 10 error. Then you can make rough but reasonable estimates and hope to be OK.
For playgrounds I would do the following: there are about 3E8 people in the US. About 10% are of playground age (say 4-12), so 3E7. Weekends are probably the most popular time-say 25% of the children go for 1 hour each out of 12 hours available. Then at any one time there are 625,000 children at the playground. If a playground can handle 50 children, you need 12,500 playgrounds. Feel free to come up with your own numbers-I made them up very quickly. If anything, I suspect this is high in the number of children, but many playgrounds are not that busy.
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