Right-skewed distribution

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 $70/10 = 7$ and the median is $(5 + 5)/2 = 5$. 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.