The median is the middle value in a dataset. It separates the top and bottom ranges.
The general formula for the median depends on the number of observations(n) in the dataset:
- If n is odd, the median is the middle observation in an ordered list of dataset elements.
- If n is even, the median is the arithmetic mean of the middle two observations in an ordered list of dataset elements. In other words, we obtain the median for such a dataset by adding the two central values and dividing them by 2.
Let's use two sets of numbers to illustrate this concept.
1, 2, 3, 4, 5
The median of the first set is 3 because it is exactly in the center of the set. Two numbers are smaller thatn the median (1, 2), and two numbers are greater (4, 5).
1, 2, 3, 4, 5, 6
The median of this second set is 3.5. This is the arithmetic mean of the two middle values, 3 and 4. Exactly three numbers are smaller than 3.5 (1, 2, 3) and three numbers are greater (4, 5, 6).
Theoretically, any value from the interval between 3 and 4 can separate the set into two halves, but only the arithmetic mean is the true median because it is the exact midpoint of the data range.