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Home Univariate Data Measures of Location Median
See also: mean, mode, fractiles, Quartile 

Median

When considering the distribution curve (or the histogram) of a sample, the median is the location which divides the area under the curve (or the area of the histogram) into two equal halves. The relative position of the mode, the median, and the mean provides an indication of the skewness of a distribution:

The median is calculated as follows:
  • Sort all values in ascending order.
  • If the number of values is odd, take the middle number.
  • If the number of values is even, take the average of the middle two numbers.
The sum of absolute deviations of sample scores from their median is lower than the absolute deviations from any other value. Under certain circumstances the median may be a more stable measure of location than the mean. The median in particular is less prone to outliers (extreme values) than the mean. Median statistics is therefore often used with robust statistics.

Example: Calculate the median of the following values: 
4.4, 5.1, 4.1, 6.2, 5.7, 5.6, 7.0
  1. Sort the seven values: 4.1, 4.4, 5.1, 5.6, 5.7, 6.2, 7.0
  2. pick the middle value (since the number of values is odd) as the median: 5.6


Home Univariate Data Measures of Location Median