The "median" value of a series of numbers refers to the middle number when all the data is ordered sequentially. Median calculations are less affected by outliers than the normal average calculation. Outliers are extreme measurements that greatly deviate from all the other numbers, so in cases where one or more outliers would skew a standard average, median values can be used, since they resist outlier-incurred bias. As more data is added, the median might change, but it will typically not change as dramatically as an average.
Order your series of numbers from smallest to largest. As an example, say you had the numbers 5, 8, 1, 3, 155, 7, 7, 6, 7, 8. You would arrange them as 1, 3, 5, 6, 6, 7, 7, 7, 8, 155.
Look for the middle number. If there are two middle numbers, as is the case with an even number of data points, you would take the average of the two middle numbers. In the example, the middle numbers are 6 and 7. Since the average of two numbers is the sum divided by 2, you achieve a median value of 6.5.
Note that the average of the entire data set would be 20.5, so you can see the difference taking the median can make. The 155 figure is an outlier, not at all consistent with the rest of the numbers. So a median provides a better measure than an average in this case.
Keep adding numbers, in sequence, as you acquire them. To continue the example, suppose you measured five new data points as 1, 8, 7, 9, 205. You would simply add them to your list, so that it reads 1, 1, 3, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 155, 205.
Find the new median number, just like you did before. In the example, there are 15 data points, so you simply find the middle one, which is "7".
If you were using an average, you would calculate 29, which again is a sizable margin away from any of the data points.
Subtract the new median calculation from the old median to calculate the change in median values. In the example, the calculation would be 7.0 minus 6.5, which tells you the median has changed by 0.5.
If you were calculating an average, the change would be 8.5, which is a fairly large jump, and probably unjustified.
- University of Michigan: Basic Statistics
- Experiment Resources: Calculate Median
- Federal Reserve Bank of Cleveland: Median Price Changes: An Alternative Approach to Measuring Current Monetary Inflation
- Fischler School of Education and Human Resources: Measures of Central Tendency: The Mean, Median, and Mode
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