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The shape of a distribution affects the relationship between the mean, median, and mode. In a unimodal and symmetrical distribution, all three measures are very close to each other at the peak. In a bimodal distribution, the mode aligns with the tallest peak, while the mean and median fall between the peaks. In a skewed distribution, the mean is pulled in the direction of the longer tail (the skew), causing it to differ from the median. For highly skewed data, the median is generally preferred because the mean becomes an inaccurate representation of the distribution's center.

Impact of Distribution Shape on Central Tendency

In a set of four simple reaction times ($$200$$, $$250$$, $$280$$, and $$250$$ milliseconds), the mean is $$245$$ milliseconds. If one extreme outlier score of $$5,000$$ milliseconds is added, the mean rises to $$1,445$$ milliseconds. This resulting mean is greater than $$80$$% of the scores and fails to represent the typical behavior in the distribution, demonstrating why researchers prefer the median for highly skewed distributions.

Example of the Impact of Skew on the Mean

In a distribution with highly skewed data, how is the relationship between the mean and median affected, and which measure of central tendency is generally preferred?

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