Which measure of center is most appropriate for heavily skewed data sets?

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BlackTom AI · Accepted Answer

The question asks which measure of center is most appropriate for heavily skewed data sets.
First, it’s important to recall the common measures of center: the mean, the median, and the mode. The mean represents the arithmetic average and is sensitive to extreme values (outliers). In heavily skewed distributions, a few extreme values can pull the mean toward the tail, making it less representative of the typical observation.
Next, the median is the middle value when data are ordered and is robust to outliers and extreme skewness. It splits the data into two halves, so extremely large or small values have little effect on its position, making it a more reliable summary of central tendency for skewed data.
The mode is the most frequently occurring value. While it can be informative in some contexts, it does not convey the overall central tendency of a spread-out, skewed distribution and can be ambiguous when there are multiple modes or no clear peak.
In the absence of specific answer choices, we can reason that for heavily skewed data, the median typically provides a better sense of a 'typical' observation than the mean because it remains relatively stable in the presence of outliers.
If there were any outliers or an extreme tail, the mean would shift toward that tail, whereas the median would stay closer to the center of the bulk of the data.
In summary, for skewed data sets, the median is preferred as the measure of center precisely because it minimizes the influence of extreme values and accurately reflects the central tendency of the majority of observations.
Note: If you had alternative options such as the mean or mode, you would contrast their behavior under skewness—emphasizing that the mean is more affected by outliers, while the mode may not represent the center in a skewed distribution.

STAT 1450.02 SP2025 (28132) Checkpoint 2.3

Which measure of center is most appropriate for heavily skewed data sets?

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