Skewness: Deciphering the Symmetry of Distributions

Skewness is a statistical measure of the asymmetry of a distribution — whether the data leans to one side rather than being symmetrical. Along with kurtosis, it describes the shape of a distribution beyond its average and spread, and it has real significance in finance, where the shape of returns matters. This guide explains what skewness is, the types, how it relates to the mean and median, and why it matters — in plain language. It builds on the normal distribution and pairs with kurtosis, and is a core topic in quantitative qualifications like the FRM.

What is skewness?

Skewness measures how lopsided a distribution is. A perfectly symmetrical distribution — like the bell-shaped normal distribution — has zero skewness: it looks the same on both sides of its centre. When a distribution is not symmetrical — when one "tail" is longer or fatter than the other — it is skewed. Skewness tells you the direction and degree of that asymmetry, capturing something the mean and standard deviation alone cannot: which way the distribution leans, and how far.

The types of skewness

There are two directions a distribution can be skewed:

• Positive skew (right-skewed). The tail on the right side (the higher values) is longer. Most values cluster on the lower side, with a few large values stretching the tail to the right. Income distributions are a classic example — most people earn modest amounts, while a few very high earners pull the tail out to the right.
• Negative skew (left-skewed). The tail on the left side (the lower values) is longer. Most values cluster on the higher side, with a few small values stretching the tail to the left.
• Zero skew. The distribution is symmetrical, like the normal distribution.

Skewness, the mean and the median

Skewness has a useful relationship with the measures of "average." In a symmetrical distribution, the mean and median are equal. But when a distribution is skewed, they diverge, because the mean is pulled in the direction of the long tail by the extreme values, while the median is not:

• In a positively skewed distribution, the mean is typically greater than the median (the high outliers drag the mean up).
• In a negatively skewed distribution, the mean is typically less than the median.

This is why, for skewed data like incomes or house prices, the median is often a better measure of the "typical" value than the mean — the mean is distorted by the extremes.

Why skewness matters in finance

Skewness matters in finance because the shape of investment returns affects risk in ways that a simple average and standard deviation miss. Investors generally dislike negative skew — a distribution with a long left tail means occasional large losses, even if most outcomes are fine. Conversely, positive skew (occasional large gains) is often preferred. Many real financial returns exhibit skewness, so ignoring it — and assuming a symmetrical normal distribution — can understate the risk of those large adverse moves. Together with kurtosis (the fatness of the tails), skewness gives a fuller, more honest picture of an investment's risk than the average and standard deviation alone.

Why it matters for finance professionals

For anyone in risk or quantitative finance, skewness is an important concept. It captures the asymmetry of outcomes — crucial when those outcomes include the risk of large losses — and it explains why two investments with the same average and volatility can have very different real risk profiles. Understanding skewness, alongside the mean, standard deviation and kurtosis, is fundamental to describing distributions properly and a regularly examined topic in professional qualifications.

Frequently asked questions

What is skewness?

A measure of the asymmetry of a distribution — whether it leans to one side. A symmetrical distribution has zero skewness; a skewed one has a longer tail on one side.

What is the difference between positive and negative skew?

Positive (right) skew has a longer right tail, with most values low and a few high outliers (like incomes). Negative (left) skew has a longer left tail, with most values high and a few low ones.

How does skewness affect the mean and median?

In skewed data the mean is pulled towards the long tail by extreme values, while the median isn't. Positive skew usually makes the mean greater than the median; negative skew makes it lower.

Why does skewness matter in finance?

Because the shape of returns affects risk. Negative skew means occasional large losses, which investors dislike, and assuming symmetrical returns can understate that risk. Skewness, with kurtosis, gives a fuller risk picture.

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Skewness is part of describing distributions and risk properly. Learnsignal's tutor-led courses, including the FRM, develop the statistical understanding that topics like this build on — with clear teaching that makes the concepts genuinely click.