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For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%. Shown percentages are rounded theoretical probabilities intended only to approximate the empirical ...
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
An estimate of the standard deviation for N > 100 data taken to be approximately normal follows from the heuristic that 95% of the area under the normal curve lies roughly two standard deviations to either side of the mean, so that, with 95% probability the total range of values R represents four standard deviations so that s ≈ R/4.
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.
The number 21.06 was chosen because It is desired that a score of 99 correspond to the 99th percentile; The 99th percentile in a normal distribution is 2.3263 standard deviations above the mean; 99 is 49 more than 50—thus 49 points above the mean; 49/2.3263 = 21.06. Normal curve equivalents are on an equal-interval scale.
Statistics of the distribution of deviations are used as measures of statistical dispersion. A distribution with different standard deviations reflects varying degrees of dispersion among its data points. The first standard deviation from the mean in a normal distribution encompasses approximately 68% of the data.
The ABC sitcom originally starred Michael J. Fox, who left the show after four seasons following his Parkinson's diagnosis and was replaced by Charlie Sheen
The dark blue zone represents observations within one standard deviation (σ) to either side of the mean (μ), which accounts for about 68.3% of the population. 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%.