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How to Remove Outliers With a Z Score

When analyzing a data set, you may often have outliers, the points that don't seem to match the pattern of data established by the rest of the data points. They can often be seen by graphing your results, since finding the "best-fit" equation for a set of points can make the stragglers very obvious. They can be caused by measurement errors, unknown phenomena or simply inaccuracies in the experimental method. Use the z-score method to eliminate outliers.

Instructions

    • 1

      Calculate both the mean and the median of absolute deviation about the median, or MAD, of your data set. To calculate the mean, add all of the results and divide that sum by the number of data points. To calculate the median of absolute deviation about the median, subtract the mean from each data point, take the absolute value and find the median -- middle -- value of those results.

    • 2

      Calculate the z-score for each data point by subtracting the population mean from the data point, and dividing that answer by the MAD. This is that data point's modified z-score.

    • 3

      Decide how you want to determine an outlier. The heuristic test states that a data point with a modified z-score of 3.5 or more should determine an outlier. Depending on your research, you may wish to eliminate the outlier altogether, or incorporate it into your results and explain it in your research.


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