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rdapaul
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the heights of adult men at Suny Rockland have mean heights of 63.6 and a standard deviation of 2.5. What does Chebyshev's theorem tell us about the percentage of men whose heights are between 58.6 in. and 68.6 in.?
rdapaul said:the heights of adult men at Suny Rockland have mean heights of 63.6 and a standard deviation of 2.5. What does Chebyshev's theorem tell us about the percentage of men whose heights are between 58.6 in. and 68.6 in.?
Chebyshev's theorem states that for any data set, the proportion of values within k standard deviations of the mean is at least 1 - 1/k^2, where k is any positive number greater than 1. This theorem is used in statistics to determine the minimum percentage of data that falls within a certain range, regardless of the shape of the data distribution.
Chebyshev's theorem provides a minimum percentage of data within a certain range, while the empirical rule gives an estimate of the percentage of data within that range based on the assumption of a normal distribution. Chebyshev's theorem is more conservative and can be applied to any data set, while the empirical rule is more specific to a normal distribution.
Yes, Chebyshev's theorem can be used for any type of data distribution, as it makes no assumptions about the shape of the data. It only requires the mean and standard deviation of the data set.
Chebyshev's theorem provides a way to determine the minimum proportion of data within a certain range, which can be useful in identifying outliers or extreme values in a data set. It also allows for a more conservative estimate of data within a range compared to the empirical rule.
Chebyshev's theorem only provides a minimum percentage of data within a range, so it does not give an exact estimate of the data. It also assumes that the data set is unimodal, meaning it has one peak or mode. Additionally, it may not be as useful for smaller data sets, as the minimum percentage may not accurately represent the data distribution.