Right and Left Skew

Welcome back to Skewed Distributions! In the previous lesson we learned to spot asymmetric shapes with one long tail and tell them apart from the symmetric bell and the flat uniform. That was the first step, and now we are ready for the second: naming the direction of the skew correctly.

This lesson focuses on the distinction between right skew and left skew. We will learn a simple naming rule, see it applied to familiar examples, and tackle a surprisingly common mix-up that trips up even experienced readers of data. By the end, we will be able to look at any skewed distribution and confidently call it by the right name.

We already know that a skewed distribution has two visually distinct sides: one where the data piles up steeply, and one where a thinner tail stretches out. The natural follow-up question is: how do we describe which way the skew goes?

The answer is refreshingly simple. We name a skewed distribution by the direction its long tail points, not by where the bulk of the data sits. The tail is the narrator — it tells us the name. Let's see this rule in action with both directions.

A distribution is called right-skewed (or positively skewed) when its long tail extends toward the right side of the number line — that is, toward higher values. In this shape, most observations cluster on the left near smaller values, and a thin trail of uncommon, larger values stretches to the right.

Picture a histogram of restaurant meal prices at a casual dining chain. Most meals cost somewhere between $10 and $20, creating a tall cluster on the left. But a few premium specials push prices to $40 or beyond, pulling a long tail to the right. Because the tail points right, we call this distribution right-skewed.

The alternate name positively skewed comes from the number line: the tail reaches toward the positive (larger) end. Both names mean exactly the same thing.

A distribution is called left-skewed (or negatively skewed) when its long tail extends toward the left side of the number line — toward lower values. Here, most observations gather on the right near higher values, while a thinner trail of unusually low values stretches to the left.

Think about exam scores on a test that most students found fairly easy. The bulk of scores pile up near 85–100, forming a peak on the right. A handful of students scored much lower, pulling a tail toward the left. Because the tail points left, we call this distribution left-skewed.

Just as before, the alternate name negatively skewed reflects the fact that the tail reaches toward the lower (more negative) end of the number line.