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In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, 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 ...
Example of samples from two populations with the same mean but different standard deviations. Red population has mean 100 and SD 10; blue population has mean 100 and SD 50. A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
2 2s: 2 consecutive measurements exceed 2 standard deviations of the reference range, and on the same side of the mean. Inaccuracy and/or imprecision R 4s: Two measurements in the same run have a 4 standard deviation difference (such as one exceeding 2 standard deviations above the mean, and another exceeding 2 standard deviations below the mean).
An IQ score of 115 means performance one standard deviation above the mean, while a score of 85 means performance one standard deviation below the mean, and so on. [5] This "deviation IQ" method is now used for standard scoring of all IQ tests in large part because they allow a consistent definition of IQ for both children and adults.
Two (or three) out of three points in a row are more than 2 standard deviations from the mean in the same direction. There is a medium tendency for samples to be mediumly out of control. The side of the mean for the third point is unspecified.
From DasGupta's inequality it follows that for a normal distribution at least 95% lies within approximately 2.582 standard deviations of the mean. This is less sharp than the true figure (approximately 1.96 standard deviations of the mean). DasGupta has determined a set of best possible bounds for a normal distribution for this inequality. [43]
Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.
Two standard deviations from the mean (dark and medium blue) account for about 95.4%, and three standard deviations (dark, medium, and light blue) for about 99.7%. The methods given in the calculation methods section (below) are approximations for use in small-sample statistics.