Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Modeling Continuous Variables Lecture 19 Sections 6 1 6 3 1 Density Functions The Normal Distribution Robb T Koether Examples Assignment Answers to Evennumbered Exercises Hampden Sydney College Tue Sep 29 2009 Outline Modeling Continuous Variables Robb T Koether Homework Review Models 1 Homework Review 2 Models 3 Area And Probability Density Functions 4 The Normal Distribution Examples 5 Assignment 6 Answers to Even numbered Exercises Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Outline Modeling Continuous Variables Robb T Koether Homework Review Models 1 Homework Review 2 Models 3 Area And Probability Density Functions 4 The Normal Distribution Examples 5 Assignment 6 Answers to Even numbered Exercises Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Homework Review Modeling Continuous Variables Robb T Koether Homework Review Models Exercise 5 20 page 336 Consider the following two frequency plots based on two sets of data with 10 observations Frequency Plot 1 Frequency Plot 2 Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises 2 1 0 1 2 2 1 0 1 2 Note that Plot 1 can be converted to Plot 2 by moving the two blue X s Homework Review Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Exercise 5 20 page 336 a Do you think the range for Plot 1 is smaller than equal to or larger than the range for Plot 2 b Do you think the mean for Plot 1 is smaller than equal to or larger than the mean for Plot 2 c Do you think the standard deviation for Plot 1 is smaller than equal to or larger than the standard deviation for Plot 2 Explain d Check your answers to parts a b and c by computing the range mean and standard deviation for each set of data Homework Review Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Solution a The ranges are clearly equal b Both distributions are symmetric so the means are in the center at 0 Thus they are equal Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises c The two blue points in Plot 2 are closer to the mean than they are in Plot 1 so they have smaller deviations All other points are the same between the two distributions Thus Plot 2 has a smaller standard deviation Homework Review Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Solution d For Plot 1 2 2 4 0 x 0 10 SSX 4 4 1 1 0 0 1 1 4 4 range r 20 20 s 9 1 491 Homework Review Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Solution d For Plot 2 2 2 4 0 x 0 10 SSX 4 1 1 0 0 0 0 1 1 4 range r 12 12 s 9 1 155 Outline Modeling Continuous Variables Robb T Koether Homework Review Models 1 Homework Review 2 Models 3 Area And Probability Density Functions 4 The Normal Distribution Examples 5 Assignment 6 Answers to Even numbered Exercises Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Models Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Definition Mathematical model A mathematical model is a mathematical abstraction and therefore a simplification of a real situation one that retains the essential features Real situations are usually much too complicated to deal with in all their details Example Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises The bell curve is a model an abstraction of many populations Real populations have all sorts of bumps and twists and irregularities The bell curve is smooth and perfectly symmetric In statistics the bell curve is called the normal curve or normal distribution Models Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Our models will be models of distributions presented either as histograms or as continuous distributions Outline Modeling Continuous Variables Robb T Koether Homework Review Models 1 Homework Review 2 Models 3 Area And Probability Density Functions 4 The Normal Distribution Examples 5 Assignment 6 Answers to Even numbered Exercises Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises Histograms and Area Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises In a histogram frequency is represented by area Consider the following distribution of rainfall data Rainfall in 0 00 2 49 2 50 4 99 5 00 7 49 7 50 9 99 10 00 12 49 12 50 14 99 Frequency 9 12 4 2 2 1 Histograms and Area Modeling Continuous Variables 12 Robb T Koether Homework Review Area And Probability Density Functions The Normal Distribution 9 No of Years Models 6 Examples Assignment Answers to Evennumbered Exercises 3 0 0 0 2 5 5 0 7 5 10 0 Rainfall in 12 5 15 0 Histograms and Area Modeling Continuous Variables Robb T Koether Homework Review Models Area And Probability Density Functions The Normal Distribution Examples Assignment Answers to Evennumbered Exercises What is the total area of this histogram Histograms and Area Modeling Continuous Variables 12 Robb T Koether Homework Review Area And Probability Density Functions The Normal Distribution 9 No of Years Models 6 30 22 5 Examples Assignment Answers to Evennumbered Exercises 3 10 5 5 0 0 0 2 5 5 0 7 5 10 0 Rainfall in 2 5 12 5 15 0 Histograms and Area Modeling Continuous Variables Robb T Koether Homework Review Models The total area is Area And Probability Density Functions The Normal Distribution Examples Assignment
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