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

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Chapter 1: (Part 2) D i C d N l Di ib i Density Curves and Normal Distributions STAT 1181 Spring 2012 1
Density curves Here is a histogram of vocabulary scores of 947 seventh graders The smooth curve drawn over the histogram is a mathematical model called a density function called a density function. Histogram of a sample with the smoothed density curve smoothed density curve theoretically describing the population 2
Density curves A smooth curve smooth curve (density curve, f(x) ) describes the overall pattern of a distribution. f(x) - density function density function for the variable x . 3
D it i Density curves come in any imaginable shape. We try to pick a model that fits the data well 4
Properties of density curves A density curve is always on or above the is always on or above the horizontal axis. has an area of exactly 1 has an area of exactly 1 underneath it. Area between a and b proportion of all = proportion of all observations that fall between a and b 5
Uniform distributions Uniform distributions are a family of density curves defined by an upper and lower bound: U(a b) defined by an upper and lower bound: U(a,b). b x f 1 ) ( 1 a b Notice that this distribution forms a a b Notice that this distribution forms a rectangle and that the area of this rectangle is 0 b a rectangle is 1 * 0 1 a b a b 6 a b
Example 1 What percent of the What percent of the observations lie between 0.5 and 0.8? 0 5 0 8 0.5 0.8 7
Exercise 1 80 1 81 1.80, 1.81 8
Normal distributions Normal distributions are a family of symmetrical, bell- shaped density curves defined by a mean ( mu ) and a shaped density curves defined by a mean ( mu ) and a

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