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# lecture5_2slides - Statistics 528 Lecture 5 1 Statistics...

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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, bell-shaped • 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 68-95-99.7 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.

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lecture5_2slides - Statistics 528 Lecture 5 1 Statistics...

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