Left-skewed distribution

A left-skewed distribution piles up on the right and trails off toward the low values, because the skew is named for the tail rather than for the peak. Negatively skewed is the same shape under another name. Scores on an easy test look like this, and so do human lifespans in a wealthy country: a ceiling near the top bunches most of the values there while a few small ones stretch the lower tail out.

Take the ten values 12, 30, 34, 35, 36, 37, 38, 38, 39, 40. The mean is $339/10 = 33.9$ and the median is $(36 + 37)/2 = 36.5$. Nine of the ten values sit between 30 and 40, and the single 12 is what puts the mean 2.6 points below the median while leaving the median exactly where it was.

Negatively skewed does not mean the values are negative. Every number in that list is positive and the distribution is still negatively skewed, because the word describes the direction of the tail relative to the peak and not the sign of the data. The companion error is reading the label off the tall side: that graph is tallest around 38, which is precisely why it is called left-skewed.

As with a right tail, the mean coming in below the median is a reliable tendency rather than a guarantee, and data sets that break the pattern can be constructed. Use it as a check on your reading of a graph, not as a substitute for looking at one, and never announce a shape from the two centers alone when the graph is in front of you.

The summary to report is the median and the IQR, kept as a matched pair, because the low tail pulls the mean and inflates the standard deviation. When you compare two distributions and only one of them is skewed, compare medians and IQRs for both so the comparison is like for like, and say why you switched. Topic 1.9 in the Fall 2026 course is titled Comparisons of the Distributions for One Quantitative Variable.