A statistical theorem predicts that the proportion of observations within a specific interval is at least 1 minus $1/k^2$. What does k represent? The percentile rank of the data The mean of the distribution The number of standard deviations away from the mean The difference between the mean and the median
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$$\mathbf{1}-\frac{\mathbf{1}}{k^{2}}$$ For example, at least $1-1 / 2^{2}=3 / 4$ of any set of numbers lie within 2 standard deviations of the mean. Similarly, for any probability distribution, the probability that a number will lie within $k$ standard deviations of the mean is at least $1-1 / k^{2}$ . For example, if the mean is 100 and the standard deviation is 10, the probability that a number will lie within 2 standard deviations of 100, or between 80 and 120, is at least Use Chebyshev’s theorem to find the fraction of all the numbers of a data set that must lie within the following numbers of standard deviations from the mean. $$6$$
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$$\mathbf{1}-\frac{\mathbf{1}}{k^{2}}$$ For example, at least $1-1 / 2^{2}=3 / 4$ of any set of numbers lie within 2 standard deviations of the mean. Similarly, for any probability distribution, the probability that a number will lie within $k$ standard deviations of the mean is at least $1-1 / k^{2}$ . For example, if the mean is 100 and the standard deviation is 10, the probability that a number will lie within 2 standard deviations of 100, or between 80 and 120, is at least Use Chebyshev’s theorem to find the fraction of all the numbers of a data set that must lie within the following numbers of standard deviations from the mean. $$5$$
$$\mathbf{1}-\frac{\mathbf{1}}{k^{2}}$$ For example, at least $1-1 / 2^{2}=3 / 4$ of any set of numbers lie within 2 standard deviations of the mean. Similarly, for any probability distribution, the probability that a number will lie within $k$ standard deviations of the mean is at least $1-1 / k^{2}$ . For example, if the mean is 100 and the standard deviation is 10, the probability that a number will lie within 2 standard deviations of 100, or between 80 and 120, is at least Use Chebyshev’s theorem to find the fraction of all the numbers of a data set that must lie within the following numbers of standard deviations from the mean. $$4$$
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