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In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
There are several such popular "laws of statistics". The Pareto principle is a popular example of such a "law". It states that roughly 80% of the effects come from 20% of the causes, and is thus also known as the 80/20 rule. [2] In business, the 80/20 rule says that 80% of your business comes from just 20% of your customers. [3]
Sieverts's law, in physical metallurgy, is a rule to predict the solubility of gases in metals. Named after German chemist Adolf Sieverts (1874–1947). Smeed's law is an empirical rule relating traffic fatalities to traffic congestion as measured by the proxy of motor vehicle registrations and country population. After R. J. Smeed.
The Gnevyshev–Ohl rule (GO rule) is an empirical rule according to which the sum of Wolf's sunspot numbers in odd cycles with preceding even cycles (E+O) are highly correlated and the correlation is lower if even cycles and preceding odd ones (O+E) are taken (see Figure 1). [1]
For a set of empirical measurements sampled from some probability distribution, the Freedman–Diaconis rule is designed approximately minimize the integral of the squared difference between the histogram (i.e., relative frequency density) and the density of the theoretical probability distribution.
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The Italian mathematician Gerolamo Cardano (1501–1576) stated without proof that the accuracies of empirical statistics tend to improve with the number of trials. [9] [3] This was then formalized as a law of large numbers. A special form of the LLN (for a binary random variable) was first proved by Jacob Bernoulli.
In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96 , meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean .