I'm calculating the average rating from a selection of people where they rate something out of 5 stars. The mean is $4.73$ with a standard deviation of $0.55$. The breakdown is roughly:
5* | 4* | 3* | 2* | 1* 76% | 20% | 3% | 0% | 1%
- Am I correct in saying that the margin of error for the mean is $0.55$?
- Can the margin of error be communicated as $4.73 \pm 0.55$?
- Is calculating the margin of error relevant for an average of 5 star ratings? (Surely $\pm 0.55$ on a mean value of $4.73$ could mean that the error bounds take it beyond 5 out-of-five 5, for instance.)
- If I'm wrong, how would you calculate the margin of error for this type of data? What is the value of calculating the margin of error for this type of data?