# CHAPTER 1 part 2 - Chapter 1: (Part 2) Density Curves and...

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Chapter 1: (Part 2)DiCd Nl DiibiDensity Curves and Normal DistributionsSTAT 1181Spring 20121
Density curvesHere is a histogram of vocabulary scores of 947 seventh gradersThe smooth curve drawn over the histogram is amathematical modelcalled adensity functioncalled adensity function.Histogram of a sample with thesmoothed density curvesmoothed density curvetheoretically describing thepopulation2
Density curvesAsmooth curvesmooth curve(density curve, f(x) ) describes theoverall pattern of a distribution.f(x)-density functiondensity functionfor the variablex.3
DitiDensity curves come in anyimaginable shape.We try to pick a model thatfits the data well4
Properties of density curvesA density curveis always on or above theis always on or above thehorizontal axis.has an area of exactly 1has an area of exactly 1underneath it.Areabetweenaandbproportionof all=proportionof allobservations that fallbetweenaandb5
Uniform distributionsUniform distributions are a family of density curvesdefined by an upper and lower bound:U(a b)defined by an upper and lower bound:U(a,b).bxf1)(1abNotice that this distribution forms aabNotice that this distribution forms arectangle and that the area of thisrectangle is0barectangle is1*01abab6ab
Example 1What percent of theWhat percent of theobservations liebetween 0.5 and 0.8?0 50 80.50.87
Exercise1 80 1 811.80, 1.818
Normal distributionsNormal distributions are a family of symmetrical, bell-shaped density curves defined by a mean(mu) and ashaped density curves defined by a mean(mu) and a

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