The median is best used as a measure of center for data sets that are skewed or contain outliers. This is because the median is less affected by extreme values than the mean.
Here are two scenarios where the median is particularly useful:
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Skewed Distributions: If the data is not symmetrically distributed (e.g., income data where a few individuals earn significantly more than the rest), the median provides a better representation of a "typical" value.
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Data with Outliers: When a data set has outliers (values that are much higher or lower than the rest of the data), the median can give a more accurate measure of central tendency than the mean, which can be heavily influenced by those outliers.
In contrast, for symmetric distributions without outliers, the mean would be a more appropriate measure of central tendency.