Lecture 2 - TA Office Hours: Vadiraj Hombal: Thursdays...

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TA Office Hours: Vadiraj Hombal: Thursdays 4:30-6:30 PM JEC 6027
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The Sample Mode is the data value that has the highest frequency of occurrence in the sample The Modal Class is the class interval in a frequency distribution or histogram that has the highest frequency
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2 3 2 1 1 9 1 7 1 5 1 3 1 1 9 7 5 3 2 0 1 0 0 X Frequency Histogram of Bimodal Data: 3 5 7 9 11 13 15 1719 2123 X 20 10 0 Frequency
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A Sample Range , R , is the difference between the maximum and minimum observations in the sample The Sample Variance , s 2 , is the average of the squared deviations of the data values from the sample mean
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The Sample Standard Deviation , s , is the positive square root of the sample variance 2 2 1 () 1 n i i xx s n = =
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WithapopulationofsizeN,the population mean and variance are computed using: N x N x N i i N i i = = = = 1 2 2 1 ) ( µ σ
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The Empirical Rule says that for a bell- shaped, symmetric distribution: - about 68% of all data values are within one standard deviation of the mean - about 95% of all observations are within two standard deviations of the mean
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- almost all (more than 99%) of the observations are within three standard deviations of the mean.
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µ−3σ µ+3σ µ−2σ µ+2σ µ−σ µ+σ 68% 95% >99% X
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A z-score measures the number of standard deviations that a data value is from the mean. The p th Percentile of a data set is a value that has p% of the data at or below it.
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The Percentile Rank of a value is the percentage of observations in the data
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Lecture 2 - TA Office Hours: Vadiraj Hombal: Thursdays...

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