A right-skewed (positively skewed) distribution has a longer tail stretching toward higher values, so a few large values pull the mean above the median. In AP Stats, recognizing right skew tells you to prefer the median and IQR over the mean and standard deviation when describing center and spread.
Right-skewed describes the shape of a distribution where most of the data piles up on the left (lower values) and a long tail stretches out to the right (higher values). The name follows the tail, not the pile. Think of incomes, house prices, or hospital stays. Most values cluster low, but a handful of huge values stretch the distribution to the right.
That tail has consequences. Extreme high values drag the mean upward, but the median barely moves because it only cares about position, not magnitude. So in a right-skewed distribution, the mean is typically greater than the median. In Topic 4.7, this idea extends from data you collected to probability distributions of random variables. When you interpret a probability distribution (LO 4.7.B), shape is one of the three things you describe (shape, center, spread), and right skew is one of the most common shapes the exam hands you.
Right-skewed lives in Topic 4.7 (Introduction to Random Variables and Probability Distributions) in Unit 4, supporting learning objective 4.7.B, which asks you to interpret a probability distribution in terms of shape, center, and spread so you can draw conclusions about a population. But the concept actually follows you through the whole course. You first meet skewness in Unit 1 when describing histograms, it resurfaces in Unit 4 with probability distributions, and it becomes a make-or-break check in Units 5-7, where strongly skewed populations affect whether sampling distributions are approximately normal. If you can spot right skew and explain what it does to the mean and median, you can avoid the single most common interpretation trap in the course, which is treating the mean as 'typical' when a long tail is inflating it.
Mean vs. Median (Unit 1)
Right skew is the reason these two measures of center disagree. The tail's extreme high values inflate the mean while the median stays put, which is why the mean sits to the right of the median. This is also why you report the median for skewed data like incomes.
Probability Distribution (Unit 4)
Shape applies to random variables, not just samples. A probability distribution for something like 'number of defective items in a sample' can be right-skewed, and LO 4.7.B expects you to read that shape and conclude things like 'most outcomes are small, but large outcomes are possible.'
Histogram (Unit 1)
The histogram is where you actually see skewness. A right-skewed histogram has tall bars on the left and a trailing-off staircase to the right. Reading shape from a graph is step one before any mean/median reasoning.
Sampling Distributions and the CLT (Unit 5)
When a population is strongly right-skewed, small-sample means inherit that skew. The Central Limit Theorem says the sampling distribution of the sample mean becomes approximately normal only when n is large enough, so right skew is exactly the situation where the 'n ≥ 30' check earns its keep.
Multiple-choice questions love to give you a right-skewed distribution with a stated mean and standard deviation, then ask which conclusion is reasonable. For example, a waiting-time distribution with mean 12 and SD 8 that's strongly right-skewed, or a discrete distribution with mean 8.2 and median 7.5. The move you need is the same every time. Recognize that mean > median signals right skew, and that a long right tail means a few large values exist while most values sit below the mean. On FRQs, skewness shows up in graph-reading and comparison tasks. The 2021 FRQ on hospital lengths of stay and the 2025 FRQ comparing gas mileages both required describing distribution shape from a display and choosing appropriate summaries. If a distribution is right-skewed, say so explicitly, then describe center and spread using the median and IQR, and never claim a skewed distribution is approximately normal.
The skew direction names the tail, not where the data piles up. Right-skewed means the tail points right (toward high values) and the bulk of data sits on the left, with mean > median. Left-skewed is the mirror image. The tail points toward low values, the data piles up high, and the mean is dragged below the median. If you remember 'the skew follows the tail,' you won't flip them on the exam.
In a right-skewed distribution, the tail stretches toward higher values while most of the data clusters at lower values.
Right skew typically makes the mean greater than the median because extreme high values pull the mean up but barely affect the median.
For right-skewed data, the median and IQR describe center and spread better than the mean and standard deviation, which are sensitive to the tail.
Probability distributions of random variables can be right-skewed too, and interpreting that shape is exactly what LO 4.7.B asks you to do.
On exam questions, mean > median is your fastest clue that a distribution is right-skewed, and 'strongly right-skewed' is your cue not to assume normality.
Real-world right-skewed examples include incomes, house prices, waiting times, and hospital lengths of stay.
It's a distribution where the tail extends toward higher values, so most data sits at the low end with a few large values stretching right. Because of that tail, the mean is typically greater than the median.
No, it's the opposite. The data piles up on the left (lower values) and the tail stretches to the right. The skew is named after the direction of the tail, not the peak.
Right-skewed has a tail toward high values with mean > median, like incomes. Left-skewed has a tail toward low values with mean < median, like scores on an easy test where most people score high.
Most likely yes. Mean greater than median is the classic signature of right skew, because a few large values inflate the mean while the median stays anchored in the middle of the data. This exact reasoning shows up in multiple-choice questions.
Use the median (with the IQR for spread). The mean gets pulled toward the long right tail, so it overstates what a 'typical' value looks like, which is why income data is almost always reported as a median.
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