Average: Mean versus Median versus Mode

Leaving aside the notion that ‘average’ means normal and good and acceptable, we need to be clear that there are three ‘measures of central tendency,’ and that you can hide a lot of uncomfortable information by not being clear on which ‘average’ is being used.
The mean is from adding up all the values and then dividing by the number of elements
The mode is the most commonly occurring value.
The median is the middle value between the extremes.
[For a proper, technical, discussion of mean v median, see here]

So, for a group of numbers 1,1,2, 3 and 10.
The mean is 1+1+2+3+10 (17) / 5 = 3.4
The median is 2.
The mode is 1.

More sinisterly, if you have nine people with £1 each and one person with £91, then the mean is £100 divide by 10 = £10. But how much does that tell you about the income distribution within the group?