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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.
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.
Percentile. In statistics, a k-th percentile, also known as percentile score or centile, is a score below which a given percentage k of scores in its frequency distribution falls (" exclusive " definition) or a score at or below which a given percentage falls (" inclusive " definition). Percentiles are expressed in the same unit of measurement ...
Normal curve equivalent (NCE): A normalized standardized score with a mean of 50 and a standard deviation of 21.06 resulting in a near equal interval scale from 0 to 99. The NCE was developed by RMC Research Corporation in 1976 to measure the effectiveness of the Title I Program across the United States and is often used to measure gains over time.
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when and , and it is described by this probability density function (or density): The variable has a mean of 0 and a variance and standard deviation of 1.
The figure illustrates the percentile rank computation and shows how the 0.5 × F term in the formula ensures that the percentile rank reflects a percentage of scores less than the specified score. For example, for the 10 scores shown in the figure, 60% of them are below a score of 4 (five less than 4 and half of the two equal to 4) and 95% are ...
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 distribution, and by ...
In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization , where the quantiles of the different measures are brought into alignment.