Skewed to the right (positively skewed) describes a distribution where most values cluster at the lower end and a longer tail stretches toward larger values, which pulls the mean above the median and makes median and IQR the preferred summaries on the AP Statistics exam.
A distribution is skewed to the right when its tail points toward the larger values on the number line. Most of the data piles up on the left, and a few unusually big values stretch out to the right. The name comes from where the tail goes, not where the pile of data sits. That trips up a lot of people, so remember it as "the skew follows the tail."
The classic example is income. Most households earn somewhere in a middle range, but a handful of very high earners drag the tail far to the right. Those big values yank the mean upward, while the median stays put near the bulk of the data. That's why right skew almost always means mean > median, and it's why you should describe a skewed distribution with the median and IQR instead of the mean and standard deviation. The mean and standard deviation are not resistant, so the tail distorts them.
This term lives in Unit 1 (Exploring One-Variable Data), especially Topic 1.9, Comparing Distributions of a Quantitative Variable. It directly supports learning objectives 1.9.A (compare graphical representations like histograms and side-by-side boxplots on shape, center, variability, and outliers) and 1.9.B (compare summary statistics like mean and median across groups). Shape is the S in the SOCV checklist (shape, outliers, center, variability), and "skewed to the right" is the exact vocabulary the scoring guidelines look for. If you write "the data leans left" or "it's lopsided," you won't earn the point. Skew also decides which summary statistics are appropriate, which echoes through every later unit that assumes roughly symmetric or normal data.
Keep studying AP Statistics Unit 1
Mean vs. Median (Unit 1)
Right skew is the reason these two can disagree. The long right tail pulls the mean toward the big values while the median resists, so in a right-skewed distribution the mean sits above the median. AP questions love asking you to explain why, not just state it.
Outliers (Unit 1)
High outliers and right skew often travel together, since both involve unusually large values. A right-skewed histogram is your cue to check the 1.5 × IQR rule on the upper end, like in the 2021 FRQ on hospital lengths of stay.
Box Plot (Unit 1)
On a boxplot, right skew shows up as a longer right whisker and a median shifted toward the left side of the box. Side-by-side boxplots are the go-to graph when an FRQ asks you to compare two groups' shapes, exactly what 1.9.A tests.
Skewness (Unit 1)
Right skew is one half of the bigger shape vocabulary. Skewed left is its mirror image, with the tail toward small values and the mean dragged below the median. Knowing both directions lets you describe any non-symmetric distribution on sight.
Right skew shows up two main ways. In multiple choice, you'll see a histogram or boxplot and be asked to identify the shape, predict whether mean > median, or pick the right summary statistic. In FRQs, it appears in compare-the-distributions prompts like the 2021 question on hospital length of stay and the 2023 question comparing Alaskan stream samples. To earn full credit you have to (1) name the shape using the phrase "skewed to the right," (2) compare both groups using comparative language like "more skewed than," and (3) address center, variability, and unusual features, not just shape. A common follow-up asks you to explain why the mean exceeds the median for a right-skewed group. The answer is that the large values in the right tail pull the mean up while the median, the middle value, is resistant. Practice questions on salaries and pupil-teacher ratios test exactly this reasoning.
Both are named for the direction of the tail, not the peak. Skewed right means the tail stretches toward large values and the mean sits above the median. Skewed left is the mirror image, where the tail stretches toward small values and the mean drops below the median. The classic mistake is seeing the data pile on the left side of a histogram and calling it "skewed left." That's backwards. A pile on the left with a tail running right is skewed RIGHT.
Skewed to the right means the tail of the distribution points toward larger values, while most of the data clusters at the lower end.
The skew is named for the tail, so a histogram with its peak on the left and a long tail to the right is skewed right, not left.
In a right-skewed distribution the mean is greater than the median because the large tail values pull the mean upward.
For skewed data, report the median and IQR instead of the mean and standard deviation, because the median and IQR are resistant to extreme values.
On comparison FRQs, you must use the exact phrase "skewed to the right" and compare shape, center, variability, and outliers across both groups to earn full credit.
Income, house prices, and hospital lengths of stay are classic right-skewed variables, since they have a natural floor near zero but no ceiling.
It means the distribution has a longer tail stretching toward larger values, with most data clustered at the lower end. It's also called positively skewed, and it causes the mean to be larger than the median.
The mean is bigger. The few large values in the right tail pull the mean upward, while the median (the middle value) resists them. That's also why the median is the better measure of center for skewed data.
No, and this is the most common mistake. Skewed right means the TAIL is on the right, so the bulk of the data actually sits on the left side of the graph. The skew direction always follows the tail, not the peak.
Skewed right has its tail toward large values and mean > median; skewed left has its tail toward small values and mean < median. Income is a classic right-skew example, while exam scores on an easy test (most people score high, a few score low) are often left-skewed.
Use the exact phrase "skewed to the right," then address center (median), variability (IQR), and any outliers, all in context. On comparison questions like the 2021 hospital-stay FRQ, you also need explicit comparative language, such as one group being more strongly skewed or having a larger median than the other.