Chebyshev's Inequality (Statistics Question)

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To find the value of k in Chebyshev's inequality, use the formula k = √(1/p), where p represents the proportion of data within k standard deviations from the mean. For example, to determine k for 95% of the data, p would be 0.95, leading to k = √(1/0.95) ≈ 1.03. This indicates that approximately 95% of the data falls within 1.03 standard deviations from the mean. Tables or calculators can also provide exact values of k for various data proportions. Understanding this relationship is essential for applying Chebyshev's inequality effectively.
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Could someone tell me how to find the k in Chebyshev's inequality??
 
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DeadxBunny said:
Could someone tell me how to find the k in Chebyshev's inequality??
Parameter "k" is the number of standard deviations "σ" on either side of the mean "μ" for which a lower bound of the included distribution {fraction between (μ-kσ) and (μ+kσ)} is required {and given by this inequality to be (1 - 1/k2)}. See also Msg #4 at the following site (Form #1 in this Msg is most commonly used):

https://www.physicsforums.com/showthread.php?t=70789


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To find the value of k in Chebyshev's inequality, you can use the following formula: k = √(1/p), where p is the proportion of data that falls within k standard deviations from the mean. This means that if you want to find the value of k for a certain percentage of data, you can calculate p by dividing that percentage by 100. For example, if you want to find the value of k for 95% of the data, p would be 0.95 (95/100). Plugging this into the formula, k = √(1/0.95) = √1.05 ≈ 1.03. This means that 95% of the data will fall within approximately 1.03 standard deviations from the mean. Additionally, you can use a table or calculator to find the exact value of k for different proportions of data.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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