Statistics: The Art and Science of Learning from Data (4th Edition)

4th Edition

ISBN: 9780321997838

Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg

Publisher: PEARSON

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Textbook Question

Chapter 2, Problem 145CP

Using MAD to measure variability The standard deviation is the most popular measure of variability from the mean. It uses squared deviations because the ordinary deviations sum to zero. An alternative measure is the mean absolute deviation, ∑ | x − x ¯ | / n .

a. Explain why greater variability tends to result in larger values of this measure.
b. Would the MAD be more, or less, resistant than the standard deviation? Explain.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 2, Problem 144CP

Chapter 2, Problem 146CP

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Chapter 2 Solutions

Statistics: The Art and Science of Learning from Data (4th Edition)

Ch. 2.1 - Categorical/quantitative difference a. Explain the...Ch. 2.1 - U.S. married-couple households According to a...Ch. 2.1 - Identify the variable type Identify each of the...Ch. 2.1 - Categorical or quantitative? Identify each of the...Ch. 2.1 - Discrete/continuous a. Explain the difference...Ch. 2.1 - Discrete or continuous? Identify each of the...Ch. 2.1 - Discrete or continuous 2 Repeat the previous...Ch. 2.1 - Prob. 8PB Ch. 2.1 - Fatal Shark Attacks Few of the shark attacks...Ch. 2.2 - Generating Electricity In 2012 in the United...

Ch. 2.2 - What do alligators eat? The bar chart is from a...Ch. 2.2 - Prob. 12PB Ch. 2.2 - Prob. 13PB Ch. 2.2 - Prob. 14PB Ch. 2.2 - Sugar dot plot For the breakfast cereal data given...Ch. 2.2 - Prob. 16PB Ch. 2.2 - Graphing exam scores A teacher shows her class the...Ch. 2.2 - Fertility rates The fertility rate for a nation is...Ch. 2.2 - Split Stems The figure below shows the...Ch. 2.2 - Histogram for sugar For the breakfast cereal data,...Ch. 2.2 - Prob. 21PB Ch. 2.2 - Prob. 22PB Ch. 2.2 - Prob. 23PB Ch. 2.2 - Prob. 24PB Ch. 2.2 - Prob. 25PB Ch. 2.2 - Prob. 26PB Ch. 2.2 - Prob. 27PB Ch. 2.2 - Warming in Newnan, Georgia? Access the Newnan, GA...Ch. 2.3 - Median versus mean For each of the following...Ch. 2.3 - Prob. 30PB Ch. 2.3 - Prob. 31PB Ch. 2.3 - Resistance to an outlier Consider the following...Ch. 2.3 - Income and health insurance According to the U.S....Ch. 2.3 - Prob. 34PB Ch. 2.3 - Prob. 35PB Ch. 2.3 - Prob. 36PB Ch. 2.3 - Public transportationcenter The owner of a company...Ch. 2.3 - Prob. 38PB Ch. 2.3 - Prob. 39PB Ch. 2.3 - European fertility The European fertility rates...Ch. 2.3 - Sex partners A recent General Social Survey asked...Ch. 2.3 - Prob. 43PB Ch. 2.3 - Prob. 44PB Ch. 2.3 - Prob. 45PB Ch. 2.4 - Sick leave A company decides to investigate the...Ch. 2.4 - Prob. 47PB Ch. 2.4 - Prob. 48PB Ch. 2.4 - Prob. 49PB Ch. 2.4 - Exam standard deviation For an exam given to a...Ch. 2.4 - Heights For the sample heights of Georgia college...Ch. 2.4 - Histograms and standard deviation The figure shows...Ch. 2.4 - Female strength The High School Female Athletes...Ch. 2.4 - Female body weight The College Athletes data file...Ch. 2.4 - Shape of cigarette taxes A recent summary for the...Ch. 2.4 - Empirical rule and skewed, highly discrete...Ch. 2.4 - How much TV? The 2012 General Social Survey asked,...Ch. 2.4 - How many friends? A recent General Social Survey...Ch. 2.4 - Judging skew using x and s If the largest...Ch. 2.4 - Youth unemployment in the EU The Youth...Ch. 2.4 - Create data with a given standard deviation Use...Ch. 2.5 - Vacation days National Geographic Traveler...Ch. 2.5 - Youth unemployment In recent years, many European...Ch. 2.5 - Female strength The High School Female Athletes...Ch. 2.5 - Female body weight The College Athletes data file...Ch. 2.5 - Ways to measure variability The standard...Ch. 2.5 - Variability of cigarette taxes Heres the...Ch. 2.5 - Prob. 68PB Ch. 2.5 - Infant mortality Africa The Human Development...Ch. 2.5 - Prob. 70PB Ch. 2.5 - Computer use During a recent semester at the...Ch. 2.5 - Central Park temperature distribution revisited...Ch. 2.5 - Box plot for exam The scores on an exam have mean...Ch. 2.5 - Public transportation Exercise 2.37 described a...Ch. 2.5 - Prob. 75PB Ch. 2.5 - Prob. 76PB Ch. 2.5 - Prob. 77PB Ch. 2.5 - Prob. 78PB Ch. 2.5 - Prob. 79PB Ch. 2.5 - Prob. 80PB Ch. 2.5 - Prob. 81PB Ch. 2.5 - Prob. 82PB Ch. 2.6 - Great pay (on the average) The six full-time...Ch. 2.6 - Prob. 84PB Ch. 2.6 - Prob. 85PB Ch. 2.6 - Terrorism and war in Iraq In 2004, a college...Ch. 2.6 - Prob. 87PB Ch. 2.6 - Prob. 88PB Ch. 2 - Categorical or quantitative? Identify each of the...Ch. 2 - Continuous or discrete? Which of the following...Ch. 2 - Prob. 92CP Ch. 2 - Cool in China A recent survey8 asked 1200...Ch. 2 - Prob. 94CP Ch. 2 - Prob. 95CP Ch. 2 - Prob. 96CP Ch. 2 - Prob. 97CP Ch. 2 - Prob. 98CP Ch. 2 - Prob. 99CP Ch. 2 - Prob. 100CP Ch. 2 - Prob. 101CP Ch. 2 - Prob. 103CP Ch. 2 - Household net worth A study reported that in 2007...Ch. 2 - Prob. 105CP Ch. 2 - Prob. 106CP Ch. 2 - Prob. 107CP Ch. 2 - Central Park monthly temperatures The MINITAB...Ch. 2 - Prob. 109CP Ch. 2 - Female heights According to a recent report from...Ch. 2 - Energy and water consumption In parts a and b,...Ch. 2 - Prob. 112CP Ch. 2 - More hurricane damage Refer to the previous...Ch. 2 - Prob. 114CP Ch. 2 - Prob. 115CP Ch. 2 - Prob. 116CP Ch. 2 - Prob. 117CP Ch. 2 - Temperatures in Central Park Access the Central...Ch. 2 - Teachers salaries According to Statistical...Ch. 2 - Prob. 120CP Ch. 2 - What box plot do you expect? For each of the...Ch. 2 - Prob. 122CP Ch. 2 - Prob. 123CP Ch. 2 - Prob. 124CP Ch. 2 - Prob. 125CP Ch. 2 - Who was Roger Maris? Roger Maris, who spent most...Ch. 2 - Baseballs great home run hitters The Baseballs HR...Ch. 2 - Prob. 128CP Ch. 2 - Controlling asthma A study of 13 children...Ch. 2 - Prob. 130CP Ch. 2 - Youth unemployment by gender The side-by-side box...Ch. 2 - You give examples Give an example of a variable...Ch. 2 - Political conservatism and liberalism Where do...Ch. 2 - Mode but not median and mean The previous exercise...Ch. 2 - Multiple choice: GRE scores In a study of graduate...Ch. 2 - Multiple choice: Fact about s Which statement...Ch. 2 - Prob. 137CP Ch. 2 - True or false: a. The mean, median, and mode can...Ch. 2 - Bad statistic A teacher summarizes grades on an...Ch. 2 - True or false: Soccer According to a story in the...Ch. 2 - Mean for grouped data Refer to the calculation of...Ch. 2 - Prob. 142CP Ch. 2 - Range and standard deviation approximation Use the...Ch. 2 - Range the least resistant Weve seen that measures...Ch. 2 - Using MAD to measure variability The standard...Ch. 2 - Prob. 146CP Ch. 2 - Create own data For the Mean Versus Median web...

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Solution Summary: The author explains that greater variability results in larger values of the MAD, which is more resistant than the standard deviation.

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