Handbook of Descriptive Statistics/Measures of Central Tendency/Median

Median Description: The median is the value found in the middle of an ordered set of data.

Median Formula: $$(n + 1) / 2$$ (remembering the data must be ordered)

Median Example: Let's say we have the following numbers: Data Set: 1,5,3,9,8 Ordered: 1,3,5,8,9 Formula: (5 [n] + 1) / 2 = 3 Therefore, the third value in the sample, 5, is the median.

If there are an even number of values in our sample then we simply find the two values either side of the formula result and average them. For example, Data set: 1,5,3,9,8,4 Ordered: 1,3,4,5,8,9 Formula: (6 [n] + 1) / 2 = 3.5 Therefore, the simple average of the third and fourth value, 4 & 5, is our median = 4.5

The best thing about the median is it is unaffected by extreme outliers. For example, using the Bill Gates example from the previous section, the median will ignore Bill's earnings giving a 'truer' indication of the central value within a dataset.

Additional Notes: Values in the dataset can be duplicated, they don't need to be unique - all calculated the same way.