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Unformatted text preview: Statistics 528  Lecture 5 1 Statistics 528  Lecture 5 Professor Kate Calder 1 Section 1.3 cont. Normal Distributions • All normal distributions have the same shape  symmetric, unimodal, bellshaped • The mean ( μ ) and standard deviation ( σ ) completely specify a normal density curve. • The mean ( μ ) is the center of the curve. Note: mean = median (since the normal density curve is symmetric) Statistics 528  Lecture 5 Professor Kate Calder 2 • The standard deviation ( σ ) is the point at which the curve changes from falling more steeply to falling less steeply (point at which the curvature changes) Statistics 528  Lecture 5 2 Statistics 528  Lecture 5 Professor Kate Calder 3 Two normal curves Statistics 528  Lecture 5 Professor Kate Calder 4 Why the normal curve? 1. Good distribution for summarizing real data exam scores repeated measurements characteristics of biological populations 2. Good approximation to chance outcomes tossing coins 3. Statistical Inference (Central Limit Theorem) HOWEVER, not all data is normal! Always do EDA before using the normal distribution. Statistics 528  Lecture 5 3 Statistics 528  Lecture 5 Professor Kate Calder 5 Relative Frequencies 689599.7 Percent Rule For a normal distribution with mean μ and standard deviation σ , • approximately 68% of the observations fall within σ of the μ . • approximately 95% of the observations fall within 2 σ of the μ ....
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This note was uploaded on 07/26/2011 for the course STA 528 taught by Professor Calder during the Winter '09 term at Ohio State.
 Winter '09
 Calder

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