A skewed distribution is a non-symmetric distribution where one tail stretches longer than the other; the skew is named for the long tail (right-skewed = tail toward high values), and the mean gets pulled toward that tail while the median stays put, which is why mean ≠ median in skewed data.
A skewed distribution is what you get when a graph of data or probabilities isn't symmetric. One side has a long tail of values, and the skew is named after the tail, not the bump. So a right-skewed (positively skewed) distribution has its tail stretching toward high values, with most of the data piled up on the low end. A left-skewed distribution is the mirror image.
The big consequence is what skew does to your measures of center. The mean is sensitive to extreme values, so it gets dragged toward the long tail. The median just counts to the middle, so it stays anchored where the data actually pile up. In a right-skewed distribution, the mean is typically greater than the median. In Topic 4.7, this matters because interpreting a probability distribution means describing its shape, center, and spread (LO 4.7.B), and skew is one of the first shape features you should name. Real-world random variables like hospital lengths of stay, waiting times, or counts of defective items are classic right-skewed examples, since they're bounded at zero but can occasionally run very high.
Skewness lives in Topic 4.7 (Introduction to Random Variables and Probability Distributions) under Unit 4, supporting LO 4.7.A (represent the probability distribution of a discrete random variable) and LO 4.7.B (interpret a probability distribution). The CED says an interpretation should cover the shape, center, and spread of a population, and skew IS the shape part for non-symmetric data. But skew shows up everywhere in this course, not just Unit 4. You describe it when you compare histograms in Unit 1, you use it to justify choosing the median over the mean, and it tells you when you can't treat a distribution like a normal curve. If you misread skew, you'll misjudge which probabilities are 'unusual,' which is exactly what exam questions probe.
Keep studying AP Statistics Unit 4
Mean and Median (Unit 1)
This is the single most testable consequence of skew. The tail pulls the mean toward it while the median resists, so right-skewed data have mean > median. If a problem hands you a mean of 8.2 and a median of 7.5, that gap is your evidence of right skew.
Normal Distribution (Units 4-5)
The normal distribution is the perfectly symmetric benchmark that skewed distributions fail to match. You can't use empirical rule shortcuts (68-95-99.7) on strongly skewed data, which is why a waiting-time distribution with mean 12 and SD 8 can't be normal (it would imply meaningful probability of negative wait times).
Outlier (Unit 1)
Outliers and skew often travel together because a long tail is basically a breeding ground for outliers on one side. Both pull the mean and inflate the standard deviation, which is why robust measures (median, IQR) are the better summary for skewed data.
Discrete Random Variable (Unit 4)
Topic 4.7 asks you to represent a discrete random variable's distribution as a table or graph and then describe its shape. Counts like 'number of defective items in a sample' are often right-skewed because they're stuck at zero on one end but unbounded on the other.
On multiple choice, the classic move is giving you a mean, median, or standard deviation and asking what you can conclude about shape, or the reverse. For example, a right-skewed distribution with mean 8.2 and median 7.5 confirms the mean sits above the median, and a strongly right-skewed waiting-time distribution with mean 12 and SD 8 rules out normality. On FRQs, skew is a describe-and-compare skill. The 2018 FRQ Q5 (teaching-year histograms), 2021 FRQ Q1 (hospital lengths of stay, with special interest in unusually short or long stays), and 2025 FRQ Q1 (gas mileage comparisons) all reward correctly naming skew, comparing centers in context, and choosing the median/IQR when the shape is asymmetric. The rubric phrase to remember is shape, center, spread, and unusual features, in context.
A normal distribution is perfectly symmetric, so its mean and median are equal and the empirical rule applies. A skewed distribution breaks both of those properties. The most common student error is assuming you can compute z-score-based probabilities for any distribution. You can't when the distribution is strongly skewed, because the symmetric bell-curve areas don't match the lopsided reality. A quick sanity check is whether mean ± 2 SD produces impossible values (like negative wait times); if it does, the distribution can't be normal.
Skew is named for the long tail, so a right-skewed distribution has its tail pointing toward high values even though most of the data sit on the low end.
The mean gets pulled toward the long tail while the median stays near the data pile, so right skew typically means the mean is greater than the median.
For skewed distributions, report the median and IQR as your measures of center and spread because the mean and standard deviation are distorted by the tail.
You cannot apply the empirical rule or normal-curve probabilities to a strongly skewed distribution; if mean minus 2 SD goes below an impossible value like zero, normality is ruled out.
Interpreting a probability distribution on the AP exam means addressing shape, center, and spread in context (LO 4.7.B), and skew is the shape vocabulary you lead with.
Real-world variables bounded at zero, like waiting times, hospital stays, and defect counts, are usually right-skewed.
A skewed distribution is a non-symmetric distribution where one tail is longer than the other. It's right-skewed if the tail stretches toward high values and left-skewed if it stretches toward low values, and the mean gets pulled toward the longer tail.
Usually yes. The long right tail drags the mean upward while the median stays near the bulk of the data, so right skew typically gives mean > median. A distribution with mean 8.2 and median 7.5, for instance, is consistent with right skew.
No, and this is the most common mistake. Skew is named for the tail, not the peak. In a right-skewed distribution, most of the data pile up on the LEFT, and a thin tail of high values stretches to the right.
A normal distribution is symmetric with mean equal to median, and the 68-95-99.7 empirical rule applies. A skewed distribution is lopsided, its mean and median split apart, and you can't use normal-curve probability shortcuts on it.
No. The empirical rule only works for approximately normal (symmetric, bell-shaped) distributions. For a strongly right-skewed distribution like waiting times with mean 12 and SD 8, normal calculations would imply negative wait times, which is impossible.