Question

Why is the mean, but not the mode nor median, affected by outliers in a data set?

Answer 1

Mean is influenced by two things, occurrence and difference in values. Mode is influenced by one thing only, occurrence. Median is positional in rank order so only indirectly influenced by value

Explanation:

Mean: Suppose you hade the values 2,2,3,4,23

The 23 ( an outlier) being so different to the others it will drag the
mean much higher than it would otherwise have been. It may
even be a false reading or something like that. It is things such as
this that makes Statistics more of a challenge sometimes. It is
imperative that thought be given to the context of the numbers
you are investigating

Median:
The only connection between value and Median is that the values
have a direct effect on the ordering of numbers. Other than that
the Median totally ignores values but is more of 'positional thing'.
No matter the magnitude of the central value or any of the others
the Median will always be central.

Mode;
The value of greatest occurrence. This is useful to show up any
bias. One of the things that make you think of bias is skew.