The sample median is the middle value in an ordered sequence of data values. To calculate the median, sort the data values from lowest to highest, then find the value that is halfway through this ordered sequence.
If N, the number of values in the data set, is odd, then one of the data values will be the middle value. For example...
12 17 19 22 30
has a median value of 19.
If N is even, then the median value is halfway between the two values in the middle. For example...
12 17 19 22 30 40
has a median value of (19 + 22)/2 = 20.5.
The position of the median in an ordered sequence of data values can be found as follows:
median position = (N + 1)/2.
So in a sequence of five values, the median position is (5 + 1)/2 = 3. That is, the median is the value in the 3rd position. In a sequence of six values, the median position is (6 + 1)/2 = 3.5, which is to say, the median is halfway between the values in the 3rd and 4th position.
An important characteristic of the median is that half the (remaining) values in the data set are below the median and half are above it. That is, the median is at the 2nd quartile or the 50th percentile.
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