I am currently working on a project involving salary distributions across different departments. Since we have a few high-level executives, the data is heavily skewed. Should I rely on the mean for my final report, or is the median a better representation of the 'average' employee experience? I want to ensure my business statistics are accurate for the stakeholders.
3 answers
In professional data science, the median is almost always superior for skewed distributions. The mean is highly sensitive to outliers, like your executive salaries, which will pull the average upward and provide a misleading picture of the typical worker's pay. By using the median, you identify the exact middle point where 50% of employees earn more and 50% earn less. This provides a more "robust" statistic that isn't distorted by extreme values at the top end of your dataset. I’ve found that presenting both—and explaining the gap—actually helps stakeholders understand income inequality better.
That is a classic dilemma! Have you considered using a box plot to visualize the spread alongside your measures of central tendency? Sometimes seeing the interquartile range helps stakeholders visualize why the mean is being pulled away from the bulk of the data points.
For financial reporting, always go with the median if the skewness is significant. The mean will just frustrate people who feel they are being "underpaid" compared to an inflated average.
I agree with Jessica. In business analysis, accuracy in perception is just as important as mathematical accuracy. Using the median prevents the "Bill Gates walks into a bar" effect where everyone suddenly becomes a millionaire on paper.
Michael, that’s a great point! Visualizing the dispersion with a box plot makes the presence of outliers undeniable to the management team. It complements the numerical data perfectly by showing the whiskers and the density of the median. I usually include a histogram as well to show the long tail of the distribution, which justifies why we opted for the median in the executive summary.