HSC MATH 121  Lecture 19  Modeling Continuous Variables (46 pages)
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Lecture 19  Modeling Continuous Variables
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 Pages:
 46
 School:
 HampdenSydney College
 Course:
 Math 121  Statistics
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Modeling Continuous Variables Lecture 19 Section 6 1 6 3 1 Fri Feb 24 2006 Models Mathematical model An abstraction and therefore a simplification of a real situation one that retains the essential features Real situations are usually much to complicated to deal with in all their details Examples Economic models treat money as a continuous quantity even though it is discrete This is an abstraction that is incorporated into the model to make it simpler The bell curve is a model an abstraction of many populations Real populations have all sorts of bumps and twists The bell curve is smooth and perfectly symmetric Models No mathematical model is perfect A mathematical model is useful and powerful to the extent that it is a faithful representation of reality Conversely to the extent that is it not faithful to reality it can lead to false conclusions about the situation that it is supposed to model Example of a Model Use a random number generator to simulate how a pair of rolled dice will land The possible totals range from 2 to 12 Using the TI 83 which is a correct model Enter randInt 2 12 that is get a random number from 2 to 12 or Enter 2 randInt 1 6 that is double a random number from 1 to 6 or Enter randInt 1 6 randInt 1 6 that is add two random numbers from 1 to 6 Histograms and Area If a histogram is drawn appropriately then frequency is represented by area Consider the following histogram of test scores Grade Frequenc 60 69 70 79 80 89 90 99 y 3 8 9 5 Histograms and Area Frequency 10 8 6 4 2 Grade 0 60 70 80 90 100 Histograms and Area In the histogram we may replace the frequency with the proportion of the total Grade Frequency Proportion 60 69 3 0 12 70 79 8 0 32 80 89 9 0 36 90 99 5 0 20 Histograms and Area Proportion 0 40 0 30 0 20 0 10 Grade 0 60 70 80 90 100 Histograms and Area Proportion 0 40 0 30 0 20 0 10 Grade 0 60 70 80 90 100 Histograms and Area Furthermore we may divide the proportions by the width of the classes to get the density Grade Frequency
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