Median
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In probability theory and statistics, the median is a number. This number has the property that it divides a set of observed values in two equal halves, so that half of the values are below it, and half are above.
If there are a finite number of elements, the median is easy to find. The values need to be arranged in a list, lowest to highest. If there is an odd number of values, the median is the one at position (n + 1) / 2. For example, if there are 13 values, they can be arranged into two groups of 6, with the median in between, at position 7. With an even number of values, as there is no single number which divides all of the numbers to two halves, the median is defined as the mean of the two central elements. With 14 observations, this would be the mean of elements 7 and 8, which is their sum divided by 2.
[change] Median and mean
Median and mean are different in several ways. Mean is a better statistical measure in many cases, because many of the statistical tests can use mean and standard deviation of two observations to compare them, while the same comparison cannot be performed using the medians.
On the opposite, median is a better statistical measure in some cases where the variance of the values is not imporant and we only need a central measure of the values. If the maximum value of a set of numbers changes while the other numbers of this set are kept the same, the mean of this set of numbers changes, but the median does not.
One of the other advantages of median is that, it can be calculated sooner when we are studying survival data. For example, a researcher can calculate the median survival of patients with kidney transplant, when half the patients participated in his study die; in contrast, if he wants to calculate the mean survival, he must continue the study and follow all of the patients until their death.[1]
[change] References
- ↑ Dawson, B; Trapp, R (2001). Basic & Clinical Biostatistics, 4th Edition, McGrawHill.
