This bound was proved by Book and Sher in 1979 for discrete samples, and more generally by Page and Murty in 1982. Has a median value of 4.5, that is ( 4 + 5 ) / 2 is bounded by one standard deviation.

If the data set has an even number of observations, there is no distinct middle value and the median is usually defined to be the arithmetic mean of the two middle values. Has the median of 6, which is the fourth value. For example, the following list of seven numbers, If the data set has an odd number of observations, the middle one is selected. The median of a finite list of numbers is the 'middle' number, when those numbers are listed in order from smallest to greatest. For this reason, the median is of central importance in robust statistics. Median income, for example, may be a better way to describe center of the income distribution because increases in the largest incomes alone have no effect on median. The basic feature of the median in describing data compared to the mean (often simply described as the 'average') is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center.

For a data set, it may be thought of as 'the middle' value. In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. Finding the median in sets of data with an odd and even number of values For other uses, see Median (disambiguation). This article is about the statistical concept.

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