Skewness vs Symmetric 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.
Skewness
Describing data
Skewness describes the asymmetry of a distribution, meaning that one tail is longer or stretched further than the other.
A distribution is skewed when values trail off farther on one side than the other. In a right-skewed distribution the long tail points toward high values, which pulls the mean above the median; in a left-skewed distribution the reverse happens. For example, incomes are often right-skewed because a few very high earners stretch the upper tail. A useful rule of thumb is that the mean gets dragged toward the longer tail.
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.