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I have a bunch of survey responses from people all over the country. Each survey has one question: "How much do you like X?" (X isn't important here), where answers range from 0 (not at all) to 100 (a lot).

I want to group the results by (for example) State. However, when I group things by State, some of these groups have a couple hundred responses, whereas others might have fewer than 10.

I want to take an average of my results by State, but States with few responses are going to potentially be misleading.

So I've been asked to add a "confidence rating" so people can determine which averages are meaningful, which aren't, etc, and I'm not sure how to properly quantify / include this sort of metric.

Making up an example:

State             Num Responses Average Rating
Rhode Island            4            96
Texas                  124           77
Alaska                  2           100
Arizona                15            55
Washington             23            76
California             34            67

marked as duplicate by whuber Jul 9 '14 at 21:21

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    $\begingroup$ Showing standard errors or, similarly, Student confidence intervals could help the reader to give an impression of the precision of your estimates. $\endgroup$ – Michael M Jul 9 '14 at 20:09
  • $\begingroup$ How do I add "student confidence intervals"? Can you offer an example, perhaps? $\endgroup$ – KaliMa Jul 9 '14 at 20:11
  • $\begingroup$ Added a sample result layout $\endgroup$ – KaliMa Jul 9 '14 at 20:19
  • $\begingroup$ We are proud to support over 1,000 threads (and counting) referring to the standard error. You can find an account of what they are and how they are computed that suits your tastes simply by searching our site for "standard error". I have arbitrarily chosen one of the first hits as a duplicate of this question. $\endgroup$ – whuber Jul 9 '14 at 21:21