Median and Mean - Different Stories from the Same Data
Consider ten people with annual incomes of 3, 3.5, 3.8, 4, 4.2, 4.5, 4.8, 5.2, 6, and 50 million yen. The mean is 8.9 million yen while the median is 4.35 million. The mean exceeds the "typical" person's income by more than double, creating the counterintuitive situation where 9 out of 10 people earn "below average." A single outlier (50 million) pulls the mean upward.
This example is extreme, but real-world income distributions exhibit the same divergence. The mean annual salary for Japanese wage earners is 4.58 million yen, but the median is 3.96 million. Using the "average income" as a benchmark causes the majority to perceive themselves as below the norm. MyRank adopts percentiles (median-based ranking) precisely to avoid this distortion inherent in means.
Which to Use - Let the Distribution Shape Decide
Whether the mean or median is more appropriate depends on the shape of the data distribution. For approximately normal (symmetric) distributions, the two values nearly coincide and either works. Height, blood pressure, and IQ scores fall into this category.
For right-skewed distributions (positive skewness), the median better represents the "typical" value. Income, wealth, housing prices, and corporate revenue all exhibit this pattern. Left-skewed distributions (negative skewness) are rare but appear in exam scores (when many score near the maximum) or product lifetimes (when early failures create a left tail).
Why Media Prefers the Mean
News outlets overwhelmingly report means rather than medians. Several factors drive this preference. First, means are computationally simpler and intuitively easier to grasp. Second, means tend to produce larger numbers, making headlines more attention-grabbing. "Average savings of 19.01 million yen" draws more clicks than "median savings of 10.61 million yen."
Third, political intent sometimes plays a role. When emphasizing economic growth, the mean (which reflects gains at the top) is preferred; when highlighting inequality, the median (which reveals stagnation for the majority) is chosen. The same dataset can support diametrically opposed narratives. As consumers of data, we must habitually ask: "Which measure of central tendency is being reported?"
Beyond Mean and Median - Mode and Trimmed Mean
Other measures of central tendency exist. The mode (most frequent value) is useful for discrete data or multimodal distributions but becomes ambiguous for continuous data. The trimmed mean removes a fixed percentage of extreme values from both ends before averaging, offering a balance between robustness to outliers and information retention.
Figure skating's practice of discarding the highest and lowest scores is an application of the trimmed mean, designed to neutralize extreme judges. MyRank selects the appropriate measure based on each data source's characteristics: percentiles (median-based) for income, normal distribution approximation (mean-based) for height.
Practicing Representative Value Literacy
Three questions to ask whenever you encounter a statistic. First: "Is this a mean or a median?" Most figures in news and advertising fail to specify. Second: "Is the distribution symmetric or skewed?" If skewed, the mean does not reflect the majority's reality.
Third: "Where do I fall in the distribution?" Even if the mean is 5 million yen, your 4 million might be above the median (3.96 million). Any single representative value compresses an entire distribution into one number, inevitably losing information. Whenever possible, examine the full distribution (percentile breakdown) to locate your position accurately. This is precisely what MyRank provides: your place within the distribution.