Shape, skew, and outliers

Before any formula, a picture. A histogram — bars showing how often values fall in each range — reveals the shape of a dataset at a glance, and shape drives every choice you make next.

Reading the shape

Three features to name every time:

• Symmetric — the two halves mirror each other, like the bell curve. Mean and median coincide.
• Skewed — a long tail on one side. Right-skewed (tail to the right) pulls the mean above the median; left-skewed does the reverse.
• Outlier — a value sitting far from the rest. It might be an error, or the most interesting point in the data.

Why shape decides your tools

Shape isn't just description — it tells you which summary to trust:

A histogram is also where you catch problems no single number shows: two separate peaks (maybe two groups mixed together), a hard floor or ceiling, or a gap.

A note on outliers

An outlier is a question, not a verdict. Before deleting one, ask why it's there: a typo, a broken sensor — or a genuine extreme worth studying. The tallest person, the record flood, the fraud in the ledger all show up as outliers. Investigate before you erase.

Why this matters

Summary numbers can hide what a picture reveals in a second. Anscombe's famous quartet is four datasets with identical means, standard deviations, and correlations — yet wildly different shapes. Always plot the data before you trust the statistics.