Uniform 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.
Uniform distribution
Describing data
A uniform distribution is one in which every outcome or interval of equal size is equally likely, giving a flat shape.
In a uniform distribution the graph is level because no value is favored over another. For example, rolling a fair six-sided die gives each face a probability of . For a continuous uniform distribution on an interval, the density is constant and probability equals the fraction of the interval covered. A flat dotplot or histogram is the visual signature of uniformity.
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.