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If, for instance, the data set {0, 6, 8, 14} represents the ages of a population of four siblings in years, the standard deviation is 5 years. As another example, the population {1000, 1006, 1008, 1014} may represent the distances traveled by four athletes, measured in meters. It has a mean of 1007 meters, and a standard deviation of 5 meters.
In the computer generation of a pseudorandom number sequence, the aim may be to generate random numbers having a normal distribution: these can be obtained from standard normal deviates (themselves the output of a pseudorandom number sequence) by multiplying by the scale parameter and adding the location parameter.
For the normal distribution, the values less than one standard deviation from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.
In some cases, data reveals an obvious non-random pattern, as with so-called "runs in the data" (such as expecting random 0–9 but finding "4 3 2 1 0 4 3 2 1..." and rarely going above 4). If a selected set of data fails the tests, then parameters can be changed or other randomized data can be used which does pass the tests for randomness.
For highly communicable epidemics, such as SARS in 2003, if public intervention control policies are involved, the number of hospitalized cases is shown to satisfy the log-normal distribution with no free parameters if an entropy is assumed and the standard deviation is determined by the principle of maximum rate of entropy production. [67]
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 ...
This is the smallest value for which we care about observing a difference. Now, for (1) to reject H 0 with a probability of at least 1 − β when H a is true (i.e. a power of 1 − β), and (2) reject H 0 with probability α when H 0 is true, the following is necessary: If z α is the upper α percentage point of the standard normal ...
Blum Blum Shub takes the form + =, where M = pq is the product of two large primes p and q.At each step of the algorithm, some output is derived from x n+1; the output is commonly either the bit parity of x n+1 or one or more of the least significant bits of x n+1.