95 percent of measurements are less than 2 standard deviations away from the mean, assuming a normal distribution.
My best estimate is around 1.5 standard deviations away from the norm.
Z-Score.
49
Standard deviation helps business understand the research they have done on their potential customers. If the information deviates by one, then they know that they can rely on the information more so than research that deviates to standards deviations away from the mean.
The Empirical Rule applies solely to the NORMAL distribution, while Chebyshev's Theorem (Chebyshev's Inequality, Tchebysheff's Inequality, Bienaymé-Chebyshev Inequality) deals with ALL (well, rather, REAL-WORLD) distributions. The Empirical Rule is stronger than Chebyshev's Inequality, but applies to fewer cases. The Empirical Rule: - Applies to normal distributions. - About 68% of the values lie within one standard deviation of the mean. - About 95% of the values lie within two standard deviations of the mean. - About 99.7% of the values lie within three standard deviations of the mean. - For more precise values or values for another interval, use a normalcdf function on a calculator or integrate e^(-(x - mu)^2/(2*(sigma^2))) / (sigma*sqrt(2*pi)) along the desired interval (where mu is the population mean and sigma is the population standard deviation). Chebyshev's Theorem/Inequality: - Applies to all (real-world) distributions. - No more than 1/(k^2) of the values are more than k standard deviations away from the mean. This yields the following in comparison to the Empirical Rule: - No more than [all] of the values are more than 1 standard deviation away from the mean. - No more than 1/4 of the values are more than 2 standard deviations away from the mean. - No more than 1/9 of the values are more than 3 standard deviations away from the mean. - This is weaker than the Empirical Rule for the case of the normal distribution, but can be applied to all (real-world) distributions. For example, for a normal distribution, Chebyshev's Inequality states that at most 1/4 of the values are beyond 2 standard deviations from the mean, which means that at least 75% are within 2 standard deviations of the mean. The Empirical Rule makes the much stronger statement that about 95% of the values are within 2 standard deviations of the mean. However, for a distribution that has significant skew or other attributes that do not match the normal distribution, one can use Chebyshev's Inequality, but not the Empirical Rule. - Chebyshev's Inequality is a "fall-back" for distributions that cannot be modeled by approximations with more specific rules and provisions, such as the Empirical Rule.
Z-Score tells how many standard deviations a measurement is away from the mean.
the Z score, or standard score.
z score
z score
z-score
My best estimate is around 1.5 standard deviations away from the norm.
Z-Score.
z
0.674 sd.
Z-score
The answer depends on the individual measurement in question as well as the mean and standard deviation of the data set.
An IQ of 130 is considered "moderatley gifted." It's basically two standard deviations away from the norm (100).