Skew is the asymmetry of a distribution, named for the direction of its longer tail. A right-skewed (positive) distribution has a tail stretching toward high values and usually mean > median; a left-skewed (negative) distribution tails toward low values and usually mean < median (UNC-1.M.2).
Skew describes a distribution that isn't symmetric. The name always follows the tail, not the pile of data. If the long tail stretches toward higher values, the distribution is skewed right (positively skewed). If the tail stretches toward lower values, it's skewed left (negatively skewed). Think of housing prices in a neighborhood. Most homes cluster at moderate prices, but a few mansions drag the tail out to the right. That's right skew.
The reason AP Stats cares so much about skew is what it does to your summary statistics. The mean gets pulled toward the tail because it's calculated from every value, including the extreme ones. The median just counts positions, so it barely moves. Per UNC-1.M.2, if a distribution is skewed right, the mean is usually to the right of the median; if skewed left, the mean is usually to the left of the median. If it's roughly symmetric, mean and median sit close together. You can spot skew on a histogram (long tail on one side), a boxplot (one whisker much longer, or the median shoved toward one end of the box), or even just by comparing the mean and median numerically.
Skew lives at the heart of Topic 1.8 in Unit 1 (Exploring One-Variable Data), supporting learning objectives 1.8.A and 1.8.B. When you describe a distribution on the exam, shape is one of the four things you always address (shape, outliers, center, spread), and skew is the most common shape feature. Skew also drives your choice of summary statistics. For skewed data, median and IQR are the resistant choices; mean and standard deviation get distorted by the tail.
It comes back in Unit 9 (Topic 9.4, learning objective 9.4.C). When you verify conditions for a t-test for the slope of a regression model, you analyze residuals to check linearity and approximately equal standard deviations across x. Heavily skewed residuals or skewed response distributions are red flags that the model's conditions may not hold. So the shape vocabulary you build in Unit 1 is the same toolkit you use to vet inference procedures at the end of the course.
Keep studying AP Statistics Unit 1
Median (Unit 1)
The median is the skew-resistant measure of center. The mean chases the tail; the median stays put. That's exactly why you report median and IQR for skewed distributions, and it's the comparison UNC-1.M.2 tests directly. Given a mean noticeably bigger than the median, you should immediately suspect right skew.
Box Plot (Unit 1)
A boxplot is the fastest way to spot skew without seeing every data point. If the right whisker is much longer than the left, or the median line sits crammed against Q1, the data are skewed right. A boxplot with no upper whisker at all means Q3 equals the maximum, so the top 25% of values are bunched right at the quartile.
Outlier (Unit 1)
Skew and outliers travel together. A right-skewed dataset often has high outliers sitting in its long tail, and both pull the mean and standard deviation upward. But they're not the same thing. Skew is a property of the whole shape; outliers are individual extreme points.
Constant Variance & Regression Conditions (Unit 9)
Before running a t-test for slope (9.4.C), you check residuals for linearity and roughly constant standard deviation of y across x. Strongly skewed residuals can signal that the conditions for inference are shaky, which connects your Unit 1 shape-reading skills straight to Unit 9 inference.
Normal Distribution (Unit 1)
The normal distribution is the benchmark of zero skew. It's perfectly symmetric, so its mean and median coincide. Any time a procedure assumes approximate normality, heavy skew in a small sample is your cue that the assumption is in trouble.
Skew is a staple of FRQ Question 1, which almost always starts with describing or comparing distributions. Released FRQs have handed you histograms of teaching years at two high schools (2018 Q5), room sizes in a residence hall (2019 Q1), hospital lengths of stay (2021 Q1), and stream chemistry data (2023 Q1). In each case, naming the skew correctly and in context is part of the shape description graders score. The 2021 prompt even flags 'unusually short or long lengths of stay,' which is skew-and-outlier language.
In multiple choice, expect stems like a boxplot with no upper whisker (what does Q3 = max tell you?), a right-skewed dataset with high outliers (which center and spread are least affected? Answer: median and IQR), or a five-number summary you have to translate into a shape claim. The classic move is giving you a mean and median and asking you to infer the direction of skew, or vice versa. Always name the skew by its tail direction and connect it to the mean-median relationship in context.
Skew is the overall shape of the distribution, a gradual stretching of one tail. Outliers are specific individual points that fall unusually far from the rest, often flagged by the 1.5×IQR rule. A distribution can be skewed with no outliers, or symmetric with one outlier. They often appear together (high outliers usually mean right skew), and both inflate the mean and standard deviation, but on the exam you describe them as separate features of the distribution.
Skew is named for the direction of the long tail, so a right-skewed distribution has its tail pointing toward high values even though most data sit on the left.
In a right-skewed distribution the mean is usually greater than the median, and in a left-skewed distribution the mean is usually less than the median (UNC-1.M.2).
For skewed data, use median and IQR as your measures of center and spread because they resist the pull of the tail and any outliers in it.
You can read skew off a boxplot by comparing whisker lengths and checking whether the median line is pushed toward one end of the box.
Skew direction questions are testable in reverse, so if you're told the mean is well above the median, you should conclude the distribution is likely skewed right.
In Unit 9, skewed residuals can signal that the conditions for a t-test for slope (linearity and constant standard deviation of y across x) are violated.
Skew is asymmetry in a distribution. A right-skewed (positive) distribution has a long tail toward high values, and a left-skewed (negative) distribution has a long tail toward low values. It's the most common shape feature you'll name when describing a distribution on the exam.
No, it's the opposite. Skew is named for the tail, not the pile. In a right-skewed distribution most data sit on the left and the long tail stretches to the right. This is the single most common skew mistake on the exam.
Skewed right usually means mean > median, because the high-value tail pulls the mean up. Skewed left usually means mean < median. If mean and median are close, the distribution is roughly symmetric (UNC-1.M.2).
Skew describes the whole distribution's shape, while outliers are individual extreme points (often found by the 1.5×IQR rule). They frequently occur together, like housing prices with a few high-value outliers creating strong positive skew, but on FRQs you address shape and outliers as separate features.
Compare the whiskers and the median's position in the box. A longer right whisker or a median pushed toward Q1 suggests right skew; the mirror image suggests left skew. If a whisker is missing entirely, like Q3 equaling the maximum, the top 25% of values are packed right at that quartile.