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Lecture 6

# Lecture 6 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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© 2008 Haipeng Shen 1/29/08 Lecture 6 1 STOR 155 Introductory Statistics Lecture 6: Density Curves and Normal Distributions (I) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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© 2008 Haipeng Shen 1/29/08 Lecture 6 2 A problem about Standard Deviation A variable has 5 values. The mean is 125 and the standard deviation is 25. If a sixth number of 125 is added in, what is the new standard deviation?
© 2008 Haipeng Shen 1/29/08 Lecture 6 3 A Tool Kit for Describing Dist. of Single Quan. Var. Plot your data: Stemplot, histogram, time plot, boxplot Look for overall pattern (shapes) + striking deviations (outliers) Calculate appropriate numerical summaries about center and spread Mean, median, mode Range, quantiles, quartiles, standard deviation Five-number summary, boxplot IQR and outliers Make things easier with a smooth curve

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© 2008 Haipeng Shen 1/29/08 Lecture 6 4
© 2008 Haipeng Shen 1/29/08 Lecture 6 5 Probability of Score <= 6

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© 2008 Haipeng Shen 1/29/08 Lecture 6 6 Density Curve To calculate probabilities, we define a probability density function f(x) . The curve that plots f(x) is called the corresponding density curve . f(x) satisfies: f(x) >=0; The total area under the curve representing f(x) equals 1.
1/29/08 Lecture 6 7 Density Curves Describe the overall shape of distributions Idealized mathematical models for distributions Show patterns that are accurate enough for practical purposes Always on or above the horizontal axis

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Lecture 6 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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