Right-Skewed Distribution vs Left-Skewed Distribution
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Right-skewed distribution
Describing data
A right-skewed distribution has its long tail stretching toward the high values, which typically pulls the mean above the median.
Skew is named for the tail, not for the peak. A right-skewed distribution piles up on the left and trails off toward the high values, so the tail points right while the tall part of the graph sits left. Positively skewed is the same thing under another name. Waiting times, incomes, and house prices tend to look this way, because there is a hard floor at the low end and nothing much stopping the high end.
Take the ten values 2, 3, 3, 4, 5, 5, 6, 8, 12, 22. The mean is and the median is . Each of the two largest values contributes a tenth of the mean at its full size, while the median only registers that they sit above the middle position. That gap between 7 and 5 is the usual signature of a right tail.
"The graph is right-skewed because most of the data is on the right" reverses it. Most of the data in a right-skewed graph is on the left, and the right is where the few stragglers are. Read the direction from where the graph runs out, not from where it is tallest, which is why a right-skewed histogram looks like it is leaning left.
The mean-above-median pattern is a strong tendency and not a theorem, so do not use it to overrule a graph. The ten values 1, 1, 1, 2, 3, 3, 3, 3, 3, 9 have an obvious right tail and a mean of 2.9 that sits just below the median of 3. Skew is a statement about shape; the ordering of the two centers is a usually reliable consequence of it.
For a right-skewed set, report the median and the IQR rather than the mean and the standard deviation, since the tail distorts both of the latter. A single high outlier is also not the same thing as skew. Skew is a gradual thinning across the upper range, while an outlier is one value alone past a gap, and the 1.5 IQR rule is the check for the second.
Left-skewed distribution
Describing data
A left-skewed distribution has its long tail stretching toward the low values, which typically pulls the mean below the median.
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 and the median is . 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.