Symmetric Distribution vs Bimodal Distribution
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Symmetric distribution
Describing data
A symmetric distribution has a shape where the left and right sides are approximate mirror images about the center.
In a symmetric distribution, folding the graph at its center makes the two halves line up closely. For example, a normal (bell-shaped) distribution is symmetric, with values equally likely to fall the same distance above or below the center. When a distribution is symmetric with a single peak, the mean and median are about equal, so (x-bar, the mean, is roughly the median). Symmetry makes the center a natural summary of the whole distribution.
Bimodal distribution
Describing data
A bimodal distribution has two distinct peaks, showing two values or ranges where observations cluster most heavily.
A bimodal shape has two clear humps, which often signals that the data mix two different groups. For example, heights measured from a room of both children and adults may peak once near each group's typical height. Each peak is a mode, so two peaks means two modes, in contrast to a single-peaked (unimodal) distribution. When you see two modes, it is worth asking whether the data should be split into subgroups.