Symmetric Distribution vs Normal 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.
Normal distribution
Random variables and distributions
The normal distribution is a symmetric, bell-shaped density curve described by its mean and standard deviation.
The normal distribution is a bell-shaped curve centered at its mean (mu) and spread out by its standard deviation (sigma). Many natural measurements, such as heights or measurement errors, are approximately normal. For example, adult heights cluster near an average, with fewer people far above or below it. The empirical rule says about 68, 95, and 99.7 percent of the data fall within 1, 2, and 3 standard deviations of the mean.