/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 Consider the following statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 10

Consider the following statement: More than \(65 \%\) of the residents of Los Angeles earn less than the average wage for that city. Could this statement be correct? If so, how? If not, why not?

Short Answer

Expert verified
Yes, the statement could be correct, because if there are outliers (people earning significantly more than the rest of the population), they can result in a higher average wage, even though the majority of people earn less than that amount.

Step by step solution

01

Derive the concept of Average

Average or mean is a measure of central tendency and is calculated as the sum of all data points divided by the number of data points. For example, if we are looking at wages, the average wage would be calculated by summing up the wages of all residents and dividing by the total number of residents.
02

Understand the Impact of Outliers

An important concept to understand is that the average can be greatly influenced by outliers. Consider a situation where 9 people earn $50 and 1 person earns $1,000. Although the majority earn $50, the average would be $145 due to the influence of the 1 person earning significantly more than the rest.
03

Apply these Concepts to the Problem

Given the fact that outliers can skew the average in one direction, it's entirely possible for a majority (in this case over 65%) of the residents to earn less than the average wage. This could occur if there are a few residents who earn a significantly higher wage than almost everyone else, pulling the average wage upwards.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

O The paper "The Pedaling Technique of Elite Endurance Cyclists" (International Journal of Sport Biomechanics [1991]: 29-53) reported the following data on single-leg power at a high workload: $$ \begin{array}{llllllll} 244 & 191 & 160 & 187 & 180 & 176 & 174 & 205 \\ 183 & 211 & 180 & 194 & 200 & & & \end{array} $$ a. Calculate and interpret the sample mean and median. b. Suppose that the first observation had been 204 , not 244\. How would the mean and median change? c. Calculate a trimmed mean by eliminating the smallest and the largest sample observations. What is the corresponding trimming percentage? d. Suppose that the largest observation had been 204 rather than \(244 .\) How would the trimmed mean in Part (c) change? What if the largest value had been 284 ?

O Bidri is a popular and traditional art form in India. Bidri articles (bowls, vessels, and so on) are made by casting from an alloy containing primarily zinc along with some copper. Consider the following observations on copper content (\%) for a sample of Bidri artifacts in London's Victoria and Albert Museum ("Enigmas of Bidri," Surface Engineering [2005]: 333-339), listed in increasing order: \(\begin{array}{llllllllll}2.0 & 2.4 & 2.5 & 2.6 & 2.6 & 2.7 & 2.7 & 2.8 & 3.0 & 3.1\end{array}\) \(\begin{array}{llllllllll}3.2 & 3.3 & 3.3 & 3.4 & 3.4 & 3.6 & 3.6 & 3.6 & 3.6 & 3.7\end{array}\) \(\begin{array}{llllll}4.4 & 4.6 & 4.7 & 4.8 & 5.3 & 10.1\end{array}\) a. Construct a dotplot for these data. b. Calculate the mean and median copper content. c. Will an \(8 \%\) trimmed mean be larger or smaller than the mean for this data set? Explain your reasoning.

Mobile homes are tightly constructed for energy conservation. This can lead to a buildup of indoor pollutants. The paper "A Survey of Nitrogen Dioxide Levels Inside Mobile Homes" (Journal of the Air Pollution Control Association [1988]: 647-651) discussed various aspects of \(\mathrm{NO}_{2}\) concentration in these structures. a. In one sample of mobile homes in the Los Angeles area, the mean \(\mathrm{NO}_{2}\) concentration in kitchens during the summer was \(36.92 \mathrm{ppb}\), and the standard deviation was 11.34. Making no assumptions about the shape of the \(\mathrm{NO}_{2}\) distribution, what can be said about the percentage of observations between \(14.24\) and \(59.60 ?\) b. Inside what interval is it guaranteed that at least \(89 \%\) of the concentration observations will lie? c. In a sample of non-Los Angeles mobile homes, the average kitchen \(\mathrm{NO}_{2}\) concentration during the winter was \(24.76 \mathrm{ppb}\), and the standard deviation was \(17.20\). Do these values suggest that the histogram of sample observations did not closely resemble a normal curve? (Hint: What is \(\bar{x}-2 s ?)\)

Suppose that 10 patients with meningitis received treatment with large doses of penicillin. Three days later, temperatures were recorded, and the treatment was considered successful if there had been a reduction in a patient's temperature. Denoting success by \(S\) and failure by \(\mathrm{F}\), the 10 observations are \(\begin{array}{llllllllll}\mathrm{S} & \mathrm{S} & \mathrm{F} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{F} & \mathrm{F} & \mathrm{S} & \mathrm{S}\end{array}\) a. What is the value of the sample proportion of successes? b. Replace each \(\mathrm{S}\) with a 1 and each \(\mathrm{F}\) with a 0 . Then calculate \(\bar{x}\) for this numerically coded sample. How does \(\bar{x}\) compare to \(p ?\) c. Suppose that it is decided to include 15 more patients in the study. How many of these would have to be S's to give \(p=.80\) for the entire sample of 25 patients?

Suppose that your statistics professor returned your first midterm exam with only a \(z\) score written on it. She also told you that a histogram of the scores was approximately normal. How would you interpret each of the following \(z\) scores? a. \(2.2\) d. \(1.0\) b. \(0.4\) e. 0 c. \(1.8\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.