Homework ReviewVariabilityThe Standard DeviationExamplesAlternate FormulaTI-83 Standard DeviationsAssignmentAnswers to Even-numbered ExercisesStandard DeviationLecture 18Section 5.3.4Robb T. KoetherHampden-Sydney CollegeMon, Feb 15, 2010Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 1 / 45Outline1Homework Review2Variability3The Standard DeviationExamplesAlternate Formula4TI-83 Standard Deviations5Assignment6Answers to Even-numbered ExercisesRobb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 2 / 45Outline1Homework Review2Variability3The Standard DeviationExamplesAlternate Formula4TI-83 Standard Deviations5Assignment6Answers to Even-numbered ExercisesRobb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 3 / 45Exercise 5.12, page 333.The five-number summary for the distribution of income (in $1000s) forthe 200 households in your neighborhood is provided below.$25, $37, $67, $100, $250(a) Draw a basic boxplot for the income distribution in yourneighborhood.First, do not find a five-number summary of these “data.”These numbers are the five-number summary.0 50 100 150 200 250Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 4 / 45Exercise 5.12, page 333.The five-number summary for the distribution of income (in $1000s) forthe 200 households in your neighborhood is provided below.$25, $37, $67, $100, $250(a) Draw a basic boxplot for the income distribution in yourneighborhood.First, do not find a five-number summary of these “data.”These numbers are the five-number summary.0 50 100 150 200 250Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 4 / 45Exercise 5.12, page 333.The five-number summary for the distribution of income (in $1000s) forthe 200 households in your neighborhood is provided below.$25, $37, $67, $100, $250(a) Draw a basic boxplot for the income distribution in yourneighborhood.First, do not find a five-number summary of these “data.”These numbers are the five-number summary.0 50 100 150 200 250Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 4 / 45Exercise 5.12, page 333.The five-number summary for the distribution of income (in $1000s) forthe 200 households in your neighborhood is provided below.$25, $37, $67, $100, $250(a) Draw a basic boxplot for the income distribution in yourneighborhood.First, do not find a five-number summary of these “data.”These numbers are the five-number summary.0 50 100 150 200 250Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 4 / 45Exercise 5.12, page 333.(b) Suppose that your household income is $56,000. What can yousay about the percentage of households that have a higher incomethan you?$56,000 is between the first quartile and the median, so we cansay that at least one-quarter of the neighborhood, but no morethan half, have a higher income.(c) If the lowest 25% of the households will be classified as poor, whatis the minimum household income that would lead to beingclassified as not poor?You must have an income of at least $37,000 not to be classifiedas poor.Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 5 / 45Exercise 5.12, page 333.(b) Suppose that your household income is $56,000. What can yousay about the percentage of households that have a higher incomethan you?$56,000 is between the first quartile and the median, so we cansay that at least one-quarter of the neighborhood, but no morethan half, have a higher income.(c) If the lowest 25% of the households will be classified as poor, whatis the minimum household income that would lead to beingclassified as not poor?You must have an income of at least $37,000 not to be classifiedas poor.Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 5 / 45Exercise 5.12, page 333.(b) Suppose that your household income is $56,000. What can yousay about the percentage of households that have a higher incomethan you?$56,000 is between the first quartile and the median, so we cansay that at least one-quarter of the neighborhood, but no morethan half, have a higher income.(c) If the lowest 25% of the households will be classified as poor, whatis the minimum household income that would lead to beingclassified as not poor?You must have an income of at least $37,000 not to be classifiedas poor.Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 5 / 45Exercise 5.12, page 333.(b) Suppose that your household income is $56,000. What can yousay about the percentage of households that have a higher incomethan you?$56,000 is between the first quartile and the median, so we cansay that at least one-quarter of the neighborhood, but no morethan half, have a higher income.(c) If the lowest 25% of the households will be classified as poor, whatis the minimum household income that would lead to beingclassified as not poor?You must have an income of at least $37,000 not to be classifiedas poor.Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 5 / 45Outline1Homework Review2Variability3The Standard DeviationExamplesAlternate Formula4TI-83 Standard Deviations5Assignment6Answers to Even-numbered ExercisesRobb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 6 / 45VariabilityOur ability to estimate a parameter accurately depends on thevariability of the estimator.That, in turn, depends on the variability that is inherent in thepopulation.The more variability in the population, the more variable theestimator.What do we mean by “variability” in the population?How do we measure it?Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 7 / 45VariabilityOur ability to estimate a parameter accurately depends on thevariability of the estimator.That, in turn, depends on the variability that is inherent in thepopulation.The more variability in the population, the more variable theestimator.What do we mean by “variability” in the population?How do we measure it?Robb T. Koether (Hampden-Sydney College) Standard Deviation Mon, Feb 15, 2010 7 / 45VariabilityOur ability to estimate a parameter accurately depends on thevariability of the estimator.That, in turn, depends on the variability that is inherent in thepopulation.The more variability in the population, the more variable theestimator.What do we mean by “variability” in the population?How do we measure
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