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No, median is not an outlier.
The mean is "pushed" in the direction of the outlier. The standard deviation increases.
An outlier can increase or decrease the mean and median It usually doesn't affect the mode
An outlier will pull the mean and median towards itself. The extent to which the mean is affected will depend on the number of observations as well as the magnitude of the outlier. The median will change by a half-step.
An outlier is a number that is very high or very low from the others. For example: 10, 15, 20, 5, 25, 25, 20, 50. Its mean would be 21.25, because the 50 is the numbers' outlier.