Yes. If you have very high or very low outliers in your data set, it is generally preferred to use the median - the mid-point when all data points are arranged from least to greatest.
A good example for when to avoid the mean and prefer the median is salary. The mean is less good here as there are a few very high salaries which skew the distribution to the right. This drags the mean higher to the point where it is disproportionately affected by the few higher salaries. In this case, the median would only be slightly affected by the few high salaries and is a better representation of the whole of the data.
In general, if the distribution is not normal, the mean is less appropriate than the median.
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An outlier does affect the mean of the data. How it's affected depends on how many data points there are, how far from the data the outlier is, whether it is greater than the mean (increases mean) or less than the mean (decreases the mean).
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.
The median is least affected by an extreme outlier. Mean and standard deviation ARE affected by extreme outliers.
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