Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q110E (page 125)

Rankings of research universities.Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 2.43 (p. 95). Recall that data on academic reputation score, financial aid awarded, and net cost to attend for the top 50 research universities are saved in the TOPUNIV file. The 50 academic reputation scores are listed in the accompanying table.

99 92 94 95 97 91 91 92 92 89 84 85 100 87 83 83 89 79 94 79 79 87 76 67 76 76 76 70 74 64 74 69 66 72 65 76 64 65 61 69 62 69 52 64 64 47 60 57 63 62

a.Find the median, lower quartile, and upper quartile for the data.

b.Find IQR for the data.

c.Graph the data with a box plot.

d.Do you detect any outliers? Suspect outliers?

Short Answer

Expert verified

(a) Median = 76, lower quartile = 64.75, upper quartile = 89.25

(b) IQR = 24.5

(c)

(d) No

Step by step solution

01

Finding the median, lower quartile, and upper quartile

Arranging the data in ascending order,

(47,52,57,60,61,62,62,63,64,64,64,64,65,65,66,67,69,69,69,70,72,74,74,76,76,76,76,76,79,79,79,83,83,84,85,87,87,89,89,91,91,92,92,92,94,94,95,97,99,100)Q1=N+14=50+14=514=12.75thterm=64.75Q2=N+12=50+12=512=25.5thterm=76Q3=3N+14=350+14=1534=38.25thterm=89.25

Therefore, Median = 76, lower quartile = 64.75, upper quartile = 89.25

02

Computing the IQR

IQR = QU – QL

= 89.25 – 64.75

= 24.5

03

Constructing the box plot

Lower Inner Fence = QL - 1.5(IQR)

= 64.75 – 1.5(24.5)

= 64.75 – 36.75

= 28

Upper Inner Fence = QU + 1.5(IQR)

= 89.25 + 1.5(24.5)

= 89.25 + 24.5

= 113.75

04

Detecting outliers and Suspect outliers

No, I do not detect any outliers or suspect outliers.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Question: For a set of data with a mound-shaped relative frequency distribution, what can be said about the percentage of the measurements contained in each of the intervals specified in Exercise 2.72?

Question: Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this feasible? Explain

Answer the following questions about the variability of data sets:

a.What is the primary disadvantage of using the range to compare the variability of data sets?

b.Describe the sample variance using words rather than a formula. Do the same with the population variance.

c.Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain.

Nuclear power plants.According to the Nuclear Energy Institute (NEI), 62 nuclear power plants were operating in the United States in 2015. The table at top of the next column lists the 30 states that operate nuclear power

plants, the number of plants in each state, and whether the state has passed legislation supporting nuclear energy expansion (regulated) or not (deregulated).

a.Find the mean, median, and mode of the number of power plants per state. Interpret these values.

b.Repeat part afor the regulated states only.

c.Repeat part afor the deregulated states only.

d.Compare the results, parts band c.What inference can you make about the impact that state regulation has on the number of nuclear power plants?

e.Eliminate the state with the largest number of power plants from the data set and repeat part a.What effect does dropping this measurement have on the measures of central tendency found in part a?

f.Arrange the 30 values in the table from lowest to highest. Next, eliminate the lowest two values and the highest two values from the data set and find the mean of the remaining data values. The result is called a 10% trimmed meanbecause it is calculated after removing the highest 10% and the lowest 10% of the data values. What advantages does a trimmed mean have over the regular arithmetic mean?

State

Status

Number of Power Plants

Alabama

Regulated

2

Arizona

Regulated

1

Arkansas

Regulated

1

California

Regulated

1

Connecticut

Deregulated

1

Florida

Regulated

3

Georgia

Regulated

2

Illinois

Deregulated

6

Iowa

Deregulated

1

Kansas

Regulated

1

Louisiana

Regulated

2

Maryland

Deregulated

1

Massachusetts

Deregulated

1

Michigan

Deregulated

3

Minnesota

Regulated

2

Mississippi

Regulated

1

Missouri

Regulated

1

Nebraska

Regulated

2

New Hampshire

Deregulated

1

New Jersey

Deregulated

3

New York

Deregulated

4

North Carolina

Regulated

3

Ohio

Deregulated

2

Pennsylvania

Deregulated

5

South Carolina

Regulated

4

Tennessee

Regulated

2

Texas

Deregulated

2

Virginia

Regulated

2

Washington

Regulated

1

Wisconsin

Deregulated

1

Budget lapsing at army hospitals.Accountants use the term budget lapsingto describe the situation that occurs when unspent funds do not carry over from one budgeting period to the next. Due to budget lapsing, U.S. army hospitals tend to stockpile pharmaceuticals and other supplies toward the end of the fiscal year, leading to a spike in expenditures. This phenomenon was investigated in the Journal of Management Accounting Research(Vol. 19, 2007). Data on expenses per full-timeequivalent employees for a sample of 1,751 army hospitalsyielded the following summary statistics: xbar= \(6,563,m= \)6,232, s= \(2,484, QL = \)5,309 and QU = \(7,216.

a.Interpret, practically, the measures of relative standing.

b.Compute the interquartile range, IQR, for the data.

c.What proportion of the 1,751 army hospitals have expenses between \)5,309 and $7,216?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

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.

Sign-up for free