Skewed to the right in AP Statistics

In AP Statistics, a distribution is skewed to the right (positively skewed) when its right tail, toward larger values, is longer than its left tail. Most data cluster at lower values, and the mean is usually larger than the median (CED 1.6.A.2, 1.8.B.1).

What is Skewed to the right?

A quantitative distribution is skewed to the right when the tail on the right side (toward larger values) stretches out longer than the tail on the left. That's the official CED wording in 1.6.A.2, and it's also called positively skewed. Picture a big hump of data on the low end and a long, thinning trail of a few large values heading off to the right.

The name trips people up, so here's the rule that never fails. Skew points to the tail, not the hump. If the long tail is on the right, it's skewed right, even though most of the data sits on the left. Classic real-world examples are things with a floor at zero but no real ceiling, like incomes, wait times, or how long patients stay in a hospital. A few huge values drag the tail (and the mean) to the right.

Why Skewed to the right matters in AP® Statistics

Skewed to the right lives in Unit 1: Exploring One-Variable Data and Collecting Data, across two topics. In Topic 1.6, it's one of the shape words you use to describe a distribution under AP Stats 1.6.A. Shape is one of the four things every description needs, along with center, variability, and unusual features (1.6.A.1). Under AP Stats 1.6.B, you use that shape to justify a claim in context. In Topic 1.8, AP Stats 1.8.B connects shape to summary statistics. If a distribution is skewed right, the mean is usually larger than the median (1.8.B.1). That link is why skew matters beyond vocabulary. It tells you which measure of center and spread to trust, and it comes back later when you check conditions for inference.

How Skewed to the right connects across the course

Mean vs. Median (Unit 1)

Think of the mean as a seesaw balance point. A few huge values on the right pull it toward the tail, while the median just counts to the middle and barely moves. That's why right skew usually means mean > median, and why the median is the better center for skewed data.

Box Plot (Unit 1)

You can spot right skew on a boxplot without seeing a single data point. Look for a longer right whisker and a median that sits closer to Q1 than to Q3. The upper half of the data is more spread out, so the right side of the plot stretches.

Outliers (Unit 1)

Right-skewed data often come with high outliers flagged beyond Q3 + 1.5(IQR). Skew and outliers are separate features, though. A distribution can be skewed with no outliers. A strong description mentions both when they're present.

Inference for Means (Unit 4)

Shape comes back when you run inference for a mean. With a small sample, strong right skew or outliers in the sample data are a red flag for using t procedures. So the Unit 1 skill of reading a graph's shape becomes a condition check later.

Is Skewed to the right on the AP® Statistics exam?

Multiple choice tests skew in a few predictable ways. One is direct vocabulary, like "Which term describes a distribution where the right tail is longer than the left tail?" The more common move gives you summary statistics and asks you to infer the shape. If a town's incomes have a mean of $65,000 and a median of $45,000, the mean sits well above the median, which points to right skew. Watch for the flip, too. A median significantly greater than the mean signals left skew.

Free response questions use shape as part of a full description or comparison. The 2021 FRQ Q1 was set in the context of hospital length of stay, and the 2023 FRQ Q1 compared samples from colder and warmer Alaskan streams. In questions like these, you need to:

• Name the shape ("skewed to the right") in context ("lengths of stay are skewed right").
• Pair shape with center, variability, and any unusual features (1.6.A.1).
• Use shape to justify a choice, like reporting the median and IQR instead of the mean and standard deviation.

A bare "it's skewed" without a direction or context usually won't earn full credit.

Skewed to the right vs Skewed to the left

These are mirror images, and people mix them up because they look at the hump instead of the tail. Skewed right has the long tail toward larger values, with the data piled on the left and the mean usually above the median. Skewed left has the long tail toward smaller values, with the data piled on the right and the mean usually below the median. Remember that the tail tells the direction. Wherever the long tail points, that's the skew.

Key things to remember about Skewed to the right

• A distribution is skewed to the right when its right tail, toward larger values, is longer than its left tail.

• The direction of skew is named for the long tail, not for where most of the data piles up.

• In a right-skewed distribution, the mean is usually larger than the median because extreme high values pull the mean toward the tail.

• For strongly skewed data, the median and IQR are better summaries of center and spread than the mean and standard deviation.

• On a boxplot, right skew often shows up as a longer right whisker and a median closer to Q1 than to Q3.

• Always describe skew in context and alongside center, variability, and unusual features to earn full FRQ credit.

Frequently asked questions about Skewed to the right

What does skewed to the right mean in AP Stats?

It means the right tail of a quantitative distribution, toward larger values, is longer than the left tail. Most values cluster on the low end, and a few large values stretch out to the right. The CED also calls this positively skewed (1.6.A.2).

Does skewed right mean most of the data is on the right?

No. Most of the data is actually on the left. The name comes from the long tail, which points right. If you remember "the skew follows the tail," you won't get this backwards.

Is the mean always bigger than the median in a right-skewed distribution?

Usually, but not always. The CED says the mean is "usually" larger than the median when a distribution is skewed right (1.8.B.1). So treat mean > median as strong evidence of right skew, not a guaranteed rule.

How is skewed right different from skewed left?

Skewed right has a long tail toward larger values and a mean usually above the median. Skewed left has a long tail toward smaller values and a mean usually below the median. For example, a mean of $65,000 with a median of $45,000 points to right skew, while a median well above the mean points to left skew.

How do you tell if a boxplot is skewed to the right?

Look for a right whisker that's noticeably longer than the left one, and a median line closer to Q1 than to Q3. Those clues mean the upper values are more spread out. That's the boxplot version of a long right tail (Topic 1.8).