An outlier is a value more than 1.5 IQRs beyond a quartile. It drags the mean and the standard deviation toward it but barely moves the median and the IQR, so a set with an outlier is reported with the median and IQR. A symmetric, single-peaked set with no outlier can be fit by a normal model: about 68% of values lie within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. A z-score counts standard deviations from the mean. A skewed set or one with an outlier should not be fit this way.