A distribution is skewed right when most values pile up on the low end and a long tail stretches toward higher values, pulling the mean above the median. In AP Stats, you describe skew when comparing distributions, and every geometric distribution is skewed right.
Skewed right (also called positively skewed) describes a distribution where most of the data sits on the left, at lower values, while a thin tail trails off to the right toward higher values. The direction of the skew is named after the tail, not the pile. That trips up a lot of people. If the tail points right, it's skewed right.
The tail matters because those few large values drag the mean upward. In a right-skewed distribution, the mean is greater than the median, since the mean gets pulled by extreme values but the median doesn't budge. Classic examples are income, house prices, and wait times. In Unit 4, this shape shows up with a guarantee attached. Every geometric distribution is skewed right, no matter what the probability of success is, because the most likely value is always x = 1 (first success on the first trial) and the probabilities shrink toward zero as x grows, creating that long right tail.
Skewed right lives in two places on the AP Stats exam. First, it's core vocabulary for describing distributions, which you do constantly when reading histograms, dotplots, and boxplots and when comparing groups. Second, it's baked into Topic 4.12, The Geometric Distribution. Learning objective 4.12.A has you calculate geometric probabilities with P(X = x) = (1-p)^(x-1)·p, and that formula is exactly why the shape is always skewed right. The first trial is the single most likely outcome, and each later trial is less likely than the one before it, so the histogram starts tall and decays to the right. When you interpret geometric parameters under 4.12.B and 4.12.C (mean = 1/p, standard deviation = √(1-p)/p), the right skew explains why the mean can feel surprisingly large. Rare successes (small p) stretch the tail way out.
Keep studying AP Statistics Unit 4
Geometric Distribution (Unit 4)
This is the one distribution on the AP exam with a built-in shape answer. Because the first success is most likely on trial 1 and probabilities decay by a factor of (1-p) each trial, every geometric distribution is skewed right. If a multiple-choice question asks the shape of a geometric distribution, the answer is always skewed right.
Mean and Median (Unit 1)
Skew tells you how the mean and median relate. In a right-skewed distribution the mean sits above the median because the long tail of high values pulls the mean toward it. This is also why the median is the better center measure for skewed data.
Outliers (Unit 1)
A long right tail and high outliers go hand in hand. Right-skewed data often has values flagged as outliers by the 1.5×IQR rule on the upper end, and those same values are what inflate the mean.
Binomial Random Variable (Unit 4)
Binomial and geometric setups look similar (independent trials, two outcomes, same p), but their shapes differ. A binomial distribution's skew depends on p, while a geometric distribution is skewed right every single time. That contrast is a favorite MCQ angle.
Skewed right shows up in two reliable ways. In multiple choice, expect shape-identification questions, especially about the geometric distribution. Stems like a network admin logging in with p = 0.25 per attempt, or a geologist drilling wells with p = 0.10 until oil is struck, ask you to recognize that the number of trials until first success is geometric and therefore skewed right with mean 1/p. In free response, skew is part of describing or comparing distributions. The 2023 FRQ on Alaskan stream chemistry asked about water samples from colder and warmer streams, the kind of question where you describe shape, center, spread, and unusual features in context. Saying "skewed right" earns shape credit only if you also address center and spread and use the variable's actual units. Also be ready to use skew as reasoning, for example explaining why the median better represents a typical value, or why mean > median in a given graph.
Skew is named after the tail, not where the data piles up. Skewed right means the tail stretches toward high values while most data sits at low values, so the mean is pulled above the median. Skewed left is the mirror image. The tail stretches toward low values, the pile sits high, and the mean falls below the median. A quick check is to find the tail and point at it. Whatever direction your finger points is the skew direction.
Skewed right means the long tail of the distribution points toward higher values, while most of the data clusters at lower values.
In a right-skewed distribution, the mean is greater than the median because extreme high values pull the mean toward the tail.
Every geometric distribution is skewed right regardless of p, because x = 1 is always the most likely number of trials and probabilities decay from there.
When p is small, the geometric mean μ = 1/p is large and the right tail stretches out farther, so rare successes mean long, skewed waits.
On FRQs, naming the shape as skewed right only earns full credit when you also describe center, spread, and any unusual features in the context of the problem.
It means most data values are low and a long tail extends toward higher values. The tail pulls the mean above the median, so for right-skewed data the mean is greater than the median.
No, and this is the most common mistake. Skew is named for the tail. In a right-skewed distribution the data piles up on the LEFT (low values) and the thin tail trails off to the RIGHT.
Yes. Because P(X = x) = (1-p)^(x-1)·p is largest at x = 1 and shrinks with every additional trial, the geometric distribution always starts tall and decays rightward. There are no symmetric or left-skewed geometric distributions.
Skewed right has the tail toward high values with mean > median; skewed left has the tail toward low values with mean < median. Income is a classic right-skew example, while exam scores on an easy test are often left-skewed.
Use the median. The mean gets dragged toward the long tail by a few large values, so it overstates a typical value. The median is resistant to skew and outliers, which is exactly the reasoning AP graders look for.
Connect this key term to the AP exam workflow: review the course, practice questions, and check related study tools.
Review units, study guides, and course resources.
Check this vocabulary in multiple-choice context.
Apply key concepts in written AP responses.
Estimate the exam score you are working toward.
Review the highest-yield facts before practice.
Put the full course together before test day.