Skewness

Statistics
definition

Also known as: skew, distribution skew

Grade 9-12

A measure of the asymmetry of a distribution — how much it leans to one side of the mean. Skewness tells you whether the mean or median is a better measure of center.

Definition

A measure of the asymmetry of a distribution — how much it leans to one side of the mean.

💡 Intuition

A right-skewed distribution has a long tail to the right (a few very large values); left-skewed has a long tail to the left.

🎯 Core Idea

Positive skew: tail on right, mean > median. Negative skew: tail on left, mean < median.

Example

Income distribution is right-skewed: most earn moderate incomes, but a few earn millions, pulling the mean up.

Formula

\text{skewness} = \frac{n}{(n-1)(n-2)} \sum\left(\frac{x_i - \bar{x}}{s}\right)^3

🌟 Why It Matters

Skewness tells you whether the mean or median is a better measure of center.

🚧 Common Stuck Point

Positive skewness means the tail extends to the right, not that most values are large.

Frequently Asked Questions

What is Skewness in Statistics?

A measure of the asymmetry of a distribution — how much it leans to one side of the mean.

Why is Skewness important?

Skewness tells you whether the mean or median is a better measure of center.

What do students usually get wrong about Skewness?

Positive skewness means the tail extends to the right, not that most values are large.

What should I learn before Skewness?

Before studying Skewness, you should understand: distribution shape.

Prerequisites

Next Steps

How Skewness Connects to Other Ideas

To understand skewness, you should first be comfortable with distribution shape. Once you have a solid grasp of skewness, you can move on to mean vs median.