The mean is "pushed" in the direction of the outlier. The standard deviation increases.
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The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
Mean 0, standard deviation 1.
Mean = 0 Standard Deviation = 1
Standard error of the mean (SEM) and standard deviation of the mean is the same thing. However, standard deviation is not the same as the SEM. To obtain SEM from the standard deviation, divide the standard deviation by the square root of the sample size.
Mean and standard deviation are not related in any way.