When you calculate a statistic the result is not going to be perfectly accurate because of random errors in your observations. You therefore can give the result as one value along with a confidence interval (CI) around it.
There are two interpretations of a CI. One interpretation is that you can be confident, with the stated level of confidence, that the true value of your statistic lies within the CI.
The other interpretation is that if you repeated your experiment then, for the stated percentage of cases, the statistic would lie within the CI.
Chat with our AI personalities
Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.
The parameters of the underlying distribution, plus the standard error of observation.
Why confidence interval is useful
You probably mean the confidence interval. When you construct a confidence interval it has a percentage coverage that is based on assumptions about the population distribution. If the population distribution is skewed there is reason to believe that (a) the statistics upon which the interval are based (namely the mean and standard deviation) might well be biased, and (b) the confidence interval will not accurately cover the population value as accurately or symmetrically as expected.
The confidence interval becomes smaller.