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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.
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value ) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Probability theory. In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while ...
Statistical significance. In statistical hypothesis testing, [1][2] a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. [3] More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that ...
If the conditions of the law of large numbers hold for the squared observations, S 2 is a consistent estimator of σ 2. One can see indeed that the variance of the estimator tends asymptotically to zero. An asymptotically equivalent formula was given in Kenney and Keeping (1951:164), Rose and Smith (2002:264), and Weisstein (n.d.). [17] [18] [19]
95% of the area under the normal distribution lies within 1.96 standard deviations away from the mean. 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 ...
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
With n = 2, the underestimate is about 25%, but for n = 6, the underestimate is only 5%. Gurland and Tripathi (1971) provide a correction and equation for this effect. [ 4 ] Sokal and Rohlf (1981) give an equation of the correction factor for small samples of n < 20. [ 5 ]