Computation of Median

For an individual (ungrouped) series the median is found by sorting the data from smallest to largest and reading off the middle value.

Locating the position. The position of the median in the ordered array is:

This formula gives the position, not the median itself; the median is then the size of the item at that position:

Odd number of items. For 5, 7, 6, 1, 8, 10, 12, 4, 3 arranged as 1, 3, 4, 5, 6, 7, 8, 10, 12 (here $N = 9$), the position is $\frac{9+1}{2} = 5^{\text{th}}$ item, so the median is 6. Half the scores are larger than 6 and half are smaller.