What Skew Looks Like

Welcome to Skewed Distributions, the fifth course in our learning path! Over the previous courses, we built a strong foundation: we learned to read distribution graphs, explored the flat uniform shape, studied the symmetric bell of the normal distribution, and counted successes with the binomial family. Now it is time to focus on distributions that break symmetry in a very recognizable way.

This first lesson is all about what skew looks like. By the end, we will be able to spot a skewed distribution at a glance and clearly tell it apart from the symmetric bell and the flat uniform shapes we already know.

Before we explore something new, let's briefly recall two important distribution shapes from earlier courses. The normal distribution forms a symmetric bell: a single peak sits in the center, and two tails trail off equally on both sides. The uniform distribution is flat, with every outcome roughly equally likely across the entire range.

Despite looking very different from each other, these two shapes share one key property: if we drew a vertical line down the middle, the left half would roughly mirror the right half. This mirror quality is what we call symmetry, and it is exactly the feature we are about to watch break.

Imagine measuring household incomes in a large city. Most households earn somewhere in a moderate range, so we see a peak on the left side of the graph. But a small number of households earn far more than the rest, stretching the graph out to the right. The result is a shape that is clearly not symmetric: one side drops off quickly while the other side extends much farther.

This kind of lopsided shape is called a skewed distribution. The hallmark of skew is a single, noticeably longer tail on one side compared to the other. Where the bell curve tapers evenly in both directions and the uniform shape stays level, a skewed distribution tilts the weight to one side and lets a thin trail of uncommon values stretch away on the other.

Two visual features set a skewed distribution apart from every other shape we have studied:

1. Asymmetry — The shape is not a mirror image around its center. One side is compressed while the other is stretched out.
2. One long tail — The bulk of the data clusters toward one end, and a thinner tail of less common values extends in the opposite direction.

Many skewed distributions look like a lopsided hill: the bulk is pushed toward one side, and a gentle slope trails off much farther on the other. Whenever we notice that contrast between a steep drop on one side and a gradual fade on the other, we are looking at skew.