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Unformatted text preview: Looking at data: distributions Density curves and Normal distributions IPS chapter 1.3 Copyright Brigitte Baldi 2005 © Objectives (IPS 1.3) Density curves and Normal distributions Density curves Normal distributions The standard Normal distribution Standardizing: calculating “zscores” Using Table A Density curves A density curve is a mathematical model of a distribution. The total area under the curve, by definition, is equal to 1, or 100%. The area under the curve for a range of values is the proportion of all observations for that range. Density curves come in any imaginable shape. Some are well known mathematically and others aren’t. Median and mean of a density curve The median of a density curve is the equalareas point, the point that divides the area under the curve in half. The mean of a density curve is the balance point, at which the curve would balance if made of solid material. The median and mean are the same for a symmetric density curve. The mean of a skewed curve is pulled in the direction of the long tail. Normal distributions Normal – or Gaussian – distributions are a family of symmetrical, bell shaped density curves defined by a mean μ ( mu ) and a standard deviation σ ( sigma ) : N( μ,σ ). x x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 A family of density curves Here means are different ( μ = 10, 15, and 20) while standard deviations are the same ( σ = 3) Here means are the same ( μ = 15) while standard deviations are different ( σ = 2, 4, and 6). mean µ = 64.5 standard deviation σ = 2.5 N(µ, σ ) = N(64.5, 2.5) All Normal curves N ( μ ,σ ) share the same properties Reminder : µ (mu) is the mean of the idealized curve, while x ¯ is the mean of a sample....
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This note was uploaded on 05/09/2009 for the course PAM 2100 taught by Professor Abdus,s. during the Spring '08 term at Cornell.
 Spring '08
 ABDUS,S.

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