I am getting a number below zero when calculating out two standard deviations from the mean. Is this ok? I am not a math wizard, so please keep your response simple enough. I need to complete a statistics screening exam for a methods course later on today, and I am hung up on one topic that came up during the practice test. The data set I got was in reference to the number of homicides that have occurred in a number of cities. The range of this data is 0-5. When I am putting together confidence intervals and calculating out as much as two standard deviations from the mean I am getting low values that are negative. Obviously you cannot have a negative number of homicides. When calculating the confidence intervals out to two standard deviations from the mean should I present the low value at ZERO or should I actually present the negative number? For example, if a 95% CI caused the calculation to be -1.5 to 3, would I present that or would I present 0 to 3? Thanks.
 A: It appears unlikely to me that the question would require you to calculate two standard deviations of the data out from the mean - especially given that your data are unlikely to be even symmetric, much less normally distributed (since they are discrete). I see no interesting question that could really be answered by this calculation.
It appears more likely that you are asked to give a confidence interval for the mean. This also involves calculating the standard deviations of the data, but then you calculate the standard error of the mean from this standard deviation by dividing by the square of the sample size and finally construct the confidence interval based on the standard error. This confidence interval is therefore much less likely to go beneath zero (and if it did, you should indeed truncate at zero). Note that the sampling distribution of the mean will be roughly normally distributed as sample size increases, which is why this interval actually answers an interesting question, namely where we expect the actual mean to lie.
