, this curve is symmetric
around a single mode
(which also happens to be the mean
.) It has inflection points
and two standard deviations
to either side of the mean. (Note: jt
shows that there's inflection points at one standard deviation on either side... I haven't checked the math yet.)
The curve is described by the following equation:
y = (1 / sqrt(2 * pi * sigma^2)) * e^(-(x - a)^2 / (2 * sigma^2))
...where a is the mean and sigma is the standard deviation.
Also known as the Gaussian or the Normal curve bell curve, or the Laplace-Gaussian curve. Karl Pearson is apparently the person responsible for the term normal, which he coined in order to avoid a naming dispute, but which he apparently now regrets since it incorrectly implies that all other distributions of data are somehow abnormal.
What does this mean to you?
Gaussian curves appear all over the place. IQ is assumed to follow a normal curve, with 100 being the mean (average), and half of the population falling above the mean, half below. Test scores for well-defined tests often fall into this shape. A lot of science, especially social science, tends to assume that data fits this pattern and chooses the statistical tests to used based on that assumption. T-tests and ANOVAs, for example, assume that the samples come from a normally distributed population.
Most statistics books contain tables at the back which list the probability that something occurs however many standard deviations away from the mean of the curve.