# statistical database calculation [closed]

Assume a database with 10,000 elements of data is queried, through a statistical interface, for the average data value. The response is determined using the random-sample query method, with a subset of 500 elements being used. Assuming you had access to all data elements, how could you determine what the least accurate response could be?

-

## closed as off-topic by bobthechemist, Kuba, RunnyKine, Yves Klett, Sjoerd C. de VriesMay 13 '14 at 20:39

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – bobthechemist, RunnyKine
If this question can be reworded to fit the rules in the help center, please edit the question.

This question appears to be off-topic. –  Sektor May 13 '14 at 15:16

You can take a sample of random selections and determine the probability of an inaccurate result.

In the example below a 'response' (e.g. mean) of less than -0.0767 or greater than 0.0767 has a small 0.27% chance of occurring.

See: 68–95–99.7 rule

elements = RandomReal[{-1, 1}, 10000];
selections = Table[RandomSample[elements, 500], {10000}];
means = Mean /@ selections;
sd = StandardDeviation[means];
Histogram[means,
Epilog -> {Line[{{-3 sd, 0}, {-3 sd, 400}}], Line[{{3 sd, 0}, {3 sd, 400}}]}]


-