Intro Stats, Books a la carte Plus NEW MyLab Statistics with Pearson eText -- Access Card Package (5th Edition)

5th Edition

ISBN: 9780134210247

Author: Richard D. De Veaux, Paul Velleman, David E. Bock

Publisher: PEARSON

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Textbook Question

Chapter 2, Problem 20E

Shoe sizes II For the shoe sizes in Exercise 16, what might be the problem with either the mean or the median as a measure of center?

16. Shoe sizes A last is a form, traditionally made of wood, in the shape of the human foot. Lasts of various sizes are used by shoemakers to make shoes. In the United States, shoe sizes are defined differently for men and women:

U.S. men’s shoe size = (last size in inches × 3) – 24

U.S. women’s shoe size = (last size in inches × 3) – 22.5

But in Europe, they are both: Euro size = last size in cm × 3/2

Here is a histogram of the European shoe sizes of 269 college students (converted from their reported U.S. shoe sizes):

Chapter 2, Problem 20E, Shoe sizes II For the shoe sizes in Exercise 16, what might be the problem with either the mean or

a) Describe the shape.
b) How many modes do you see? What might explain that?

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 19E

Chapter 2, Problem 21E

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Chapter 2 Solutions

Intro Stats, Books a la carte Plus NEW MyLab Statistics with Pearson eText -- Access Card Package (5th Edition)

Ch. 2.3 - You may be surprised to find that you already have...Ch. 2.3 - You may be surprised to find that you already have...Ch. 2.3 - You may be surprised to find that you already have...Ch. 2.3 - Prob. 4JC Ch. 2.3 - Prob. 5JC Ch. 2.5 - The U.S. Census Bureau reports the median family...Ch. 2.5 - Prob. 7JC Ch. 2.5 - Prob. 8JC Ch. 2 - SECTION 2.1 1. Automobile fatalities The table...Ch. 2 - Nonoccupant fatalities The frequencies of traffic...

Ch. 2 - Prob. 3E Ch. 2 - Movie ratings The Motion Picture Association of...Ch. 2 - Prob. 5E Ch. 2 - Marriage in decline Changing attitudes about...Ch. 2 - Traffic fatalities 2013 Here are two histograms...Ch. 2 - Prob. 8E Ch. 2 - Prob. 9E Ch. 2 - Prob. 10E Ch. 2 - E-mails A university teacher saved every e-mail...Ch. 2 - Adoptions The U.S. Census Bureau keeps track of...Ch. 2 - Biceps revisited Describe the shape of the...Ch. 2 - E-mails II For the distribution of e-mails sent by...Ch. 2 - Life expectancy Here are the life expectancies at...Ch. 2 - Prob. 16E Ch. 2 - Life expectancy II For the 146 life expectancies...Ch. 2 - Adoptions II For the number of adoptions in...Ch. 2 - How big is your bicep II? For the bicep...Ch. 2 - Shoe sizes II For the shoe sizes in Exercise 16,...Ch. 2 - SECTION 2.5 21. Life expectancy III For the 190...Ch. 2 - Prob. 22E Ch. 2 - How big is your bicep III? For the bicep...Ch. 2 - Prob. 24E Ch. 2 - Thinking about shape Would you expect...Ch. 2 - More shapes Would you expect distributions of...Ch. 2 - Movie genres again Here is a bar chart summarizing...Ch. 2 - Prob. 36E Ch. 2 - Prob. 37E Ch. 2 - Prob. 38E Ch. 2 - Prob. 39E Ch. 2 - Prob. 40E Ch. 2 - Prob. 41E Ch. 2 - Prob. 42E Ch. 2 - Prob. 43E Ch. 2 - Modalities A survey of athletic trainers asked...Ch. 2 - Cereals The histogram shows the carbohydrate...Ch. 2 - Run times One of the authors collected the times...Ch. 2 - Heart attack stays The histogram shows the lengths...Ch. 2 - Bird species 2013 The Cornell Lab of Ornithology...Ch. 2 - Super Bowl points 2016 How many points do football...Ch. 2 - Prob. 50E Ch. 2 - Test scores, large class Test scores from a large...Ch. 2 - Prob. 52E Ch. 2 - Mistake A clerk entering salary data into a...Ch. 2 - Sick days During contract negotiations, a company...Ch. 2 - Prob. 55E Ch. 2 - Tornadoes 2015 Here are the annual numbers of...Ch. 2 - Prob. 57E Ch. 2 - Tornadoes 2015 II Using the data from Exercise 56,...Ch. 2 - Pizza prices The histogram shows the distribution...Ch. 2 - Neck size The histogram shows the neck sizes (in...Ch. 2 - Pizza prices again Look again at the histogram of...Ch. 2 - Neck sizes again Look again at the histogram of...Ch. 2 - Movie lengths 2010 The histogram shows the running...Ch. 2 - Golf drives 2015 The display shows the average...Ch. 2 - Prob. 65E Ch. 2 - Golf drives II 2015 Exercise 64 looked at...Ch. 2 - Prob. 67E Ch. 2 - Cold weather A meteorologist preparing a talk...Ch. 2 - Gasoline 2014 In January 2014, 16 gas stations in...Ch. 2 - The great one During his 20 seasons in the NHL,...Ch. 2 - Prob. 71E Ch. 2 - Prob. 72E Ch. 2 - Prob. 73E Ch. 2 - Prob. 74E Ch. 2 - Prob. 75E Ch. 2 - Prob. 76E Ch. 2 - Acid rain Two researchers measured the pH (a scale...Ch. 2 - Marijuana 2015 In 2015 the Council of Europe...Ch. 2 - Prob. 79E Ch. 2 - Prob. 80E Ch. 2 - Prob. 81E Ch. 2 - ZIP codes revisited Here are some summary...Ch. 2 - Prob. 83E Ch. 2 - Prob. 84E Ch. 2 - Prob. 85E

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Solution Summary: The author explains how the distribution of shoe sizes for men and women is symmetric, bimodal, and multimodal based on the number of peaks.

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