That median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half. For a data set, it may be thought of as the "middle" value. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth largest, and also the fourth smallest, number in the sample. For a continuous probability distribution, the median is the value such that a number is equally likely to fall above or below it.

The median is a commonly used measure of the properties of a data set in statistics and probability theory. The basic advantage of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed so much by extremely large or small values, and so it may give a better idea of a "typical" value. For example, in understanding statistics like household income or assets which vary greatly, a mean may be skewed by a small number of extremely high or low values. Median income, for example, may be a better way to suggest what a "typical" income is.

Because of this, the median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.

What are the answers to this following set of questions:

1. What is of great importance in robust statistics?
2. The median is a measure of what?
3. A data set within what?
4. What is the advantage of the median?
5. Skewed so much as what?
6. What other helpful measure does it give?
7. What can skew a mean?
8. In robust statistics, is the median is the most resistant statistic?
9. For a continuous probability distribution, how do you explain a median?
10. For a data set, how could you describe the median?
11. In robust statistics, the median has a breakdown point of what?
12. And can't have more than half the data, what?
13. Then what will happen?
1. The median.
2. The properties of a data set.
3. Statistics and probability theory.
4. It is not skewed so much.
5. Extremely large or small values.
6. It may give a better idea of a "typical" value.
7. By a small number of extremely high or low values.
8. Yes.
9. The value such that a number is equally likely to fall above or below it.
10. The "middle" value.
11. 50%:
12. Contaminated.
13. The median will not give an arbitrarily large or small result.