L5-ss

# L5-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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5/16/11 Lecture 5 1 STOR 155 Introductory Statistics Lecture 5: Density Curves and Normal Distributions (I) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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5/16/11 Lecture 5 2 A problem about Standard Deviation A variable has 5 possible 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?
5/16/11 Lecture 5 3 To describe distribution of variable X • Plot your data: – Stemplot, histogram, boxplot • Look for overall pattern (shapes) + striking deviations (outliers) • Calculate appropriate numerical summaries about center and spread – Mean, median, mode – Range, percentiles, quartiles, standard deviation – Five-number summary, boxplot – IQR and outliers Make things easier with a smooth curve

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5/16/11 Lecture 5 4
5/16/11 Lecture 5 5 Density Curve --- A Math Approximation • 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.

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5/16/11 Lecture 5 6 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 • The total area under the curve is exactly 1 • Areas under the curve represent relative frequencies of observations
5/16/11 Lecture 5

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## This note was uploaded on 11/18/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Summer '08 term at UNC.

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L5-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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