The dataset must be ordered before the median can be determined.
The number of items (n) will determine where the median is located.
(n+1)/2 = median rank
For example:
1 , 1 , 2 , 4 , 6 , 2 , 9 , 3 , 7 , 5 , 2 , 5 , 9 , 6
Ordered:
1 , 1 , 2 , 2 , 2 , 3 , 4 , 5 , 5 , 6 , 6 , 7 , 9 , 9
Total count:
n=14
Median rank = (14+1)/2=7.5
Since this dataset has an even number of items (n=14) then the median is found between the 7th and 8th position. The 7th value is 4, and the 8th value is 5. The value inbetween is (4+5)/2=4.5. The median is 4.5. There are 7 items above and below this value.
For datasets with odd number n, the median falls exactly on the median rank.
To illustrate:
1 , 1 , 2 , 4 , 6 , 2 , 9 , 3 , 7 , 5 , 2 , 5 , 9 , 6, 4
Ordered:
1 , 1 , 2 , 2 , 2 , 3 , 4 , 4 , 5 , 5 , 6 , 6 , 7 , 9 , 9
Median rank = (15+1)/2 = 8
The value in the 8th position is 4, so the median is 4. There are 7 items above and below it.
The mean, median, and mode are all measures of central tendency. The skew can be determined by comparing these three measures.
