What is of great importance in robust statistics?
The median.
The median is a measure of what?
The properties of a data set.
A data set within what?
Statistics and probability theory.
What is the advantage of the median?
It is not skewed so much.
Skewed so much as what?
Extremely large or small values.
What other helpful measure does it give?
It may give a better idea of a "typical" value.
What can skew a mean?
By a small number of extremely high or low values.
In robust statistics, is the median is the most resistant statistic?
Yes.
For a continuous probability distribution, how do you explain a median?
The value such that a number is equally likely to fall above or below it.
For a data set, how could you describe the median?
The "middle" value.
In robust statistics, the median has a breakdown point of what?
50%:
And can't have more than half the data, what?
Contaminated.
Then what will happen?
The median will not give an arbitrarily large or small result.