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EMPIRICAL RULE
This states that for a normal distribution nearly all values lie within 3 standard deviations of the arithmetic mean and about 68.27% of the values lie within 1 standard deviation of the mean. Similarly, about 95.45% of the values lie within 2 standard deviations of the mean and nearly all (99.73%) of the values lie within 3 standard deviations of the mean.
In mathematical notation, these facts can be expressed as follows, where x is considered as an observation from a normally distributed random variable and μ is defined as the mean of the distribution, and σ is defined as its standard deviation
Empirical Rule Homework Help
This rule is often used to quickly get a rough probability estimate of something if its standard deviation is given and if the population is assumed normal. This is a simple test for out liners if the population is assumed normal and a normality test if the population is potentially not normal.
In order to pass from a sample to a number of standard deviations, it computes the deviation which is either the errors and residuals in statistics and then it uses either standardizing that is dividing by the population standard deviation of the population parameters are known or it uses studentizing by dividing by an estimate of the standard deviation of the parameters are unknown and only estimated.
To use as a test for outliers or a normality test, one calculates the size of deviations in terms of standard deviations, and it then compares this to expected frequency. Given a sample set, it computes the studentized residual and compares these to the expected frequency and the points that fall more than 3 standard deviations from the norm are likely outliers.
This is significantly large, by which point one expects a sample this extreme and if there are many points more than 3 standard deviations from the norm, one likely can question the assumed normality of the distribution.
Empirical Rule Assignment Help
One can compute more approximately the number of extreme moves of a given magnitude or greater by using a Poisson distribution. If one has multiple 4 standard deviation moves in a sample of size 1,000, then there is a strong reason to consider these outliers or question the assumed normality of the distribution.
