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Idea Transcript
Prob & Stats
October 06, 2014
32 Measures of Variation (continued)
32 Variation (continued)
Prob & Stats
October 06, 2014
Chebyshev's Theorem ~We can do or say a lot about bellshaped or symmetric distributions ~Chebyshev's Theorem allows us to talk about the spread of data for any shape distribution
32 Variation (continued)
Prob & Stats
October 06, 2014
Chebyshev's Theorem For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least
32 Variation (continued)
Prob & Stats
October 06, 2014
What does this mean? For any set of data: ~at least 75% of the data fall within 2 standard deviations of the mean ~at least 88.9% of the data fall within 3 standard deviations of the mean ~at least 93.8% of the data fall within 4 standard deviations of the mean
32 Variation (continued)
Prob & Stats
October 06, 2014
Example: The mean price of houses in a certain neighborhood is $50,000 and the standard deviation is $10,000. Find the price range for which at least 75% of the houses will sell.
32 Variation (continued)
Prob & Stats
October 06, 2014
Example: A survey of local companies found that the mean amount of travel allowance for executives was $0.25 per mile. The standard deviation was $0.02. Using Chebyshev's theorem, find the minimum percentage of the data values that will fall between $0.20 and $0.30.
32 Variation (continued)
Prob & Stats
October 06, 2014
The Empirical Rule: If a set of data is normally distributed (bell shaped/symmetrical), then approximately: ~68% of the data fall within 1 standard deviation of the mean ~95% of the data fall within 2 standard deviations of the mean ~99.7% of the data fall within 3 standard deviations of the mean