Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.

a.The salaries of all persons employed by a large university

b.The grades on an easy test

c.The grades on a difficult test

d.The amounts of time students in your class studied last week

e.The ages of automobiles on a used-car lot

f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)

Short Answer

Expert verified

a) Rightward Skewness

b) Leftward Skewness

c) Rightward Skewness

d) Rightward Skewness

e) Leftward Skewness

f) Leftward Skewness

Step by step solution

01

Determining the skewness of the data set in (a)

The salaries of everybody employed at a large university will be skewed to the right because while the majority of the people would have an average salary, there might be some outliers who would have higher salaries.

02

Determining the skewness of the data set in (b)

The grades on an easy test will have a leftward skewed distribution because most of them would perform well on the test, but there might be only a few who would not score well.

03

Determining the skewness of the data set in (c)

The grades on a difficult test will be skewed to the right because, as it is a difficult test, only a few would do well while the majority would have performed poorly.

04

Determining the skewness of the data set in (d)

The number of time students in your class studied last week would be skewed to the right because the majority of students would study moderately, whilst there would be some that would dedicate extra time to study

05

Determining the skewness of the data set in (e)

The ages of automobiles on a used-car lot would be skewed to the left because there would mostly be a wide range of new vehicles, with only a few that have been used for a very long time.

06

Determining the skewness of the data set in (f)

The amount of time spent on a difficult examination is skewed to the left because most of the students would take the whole 50 minutes time to complete the test; some of them might be able to do it in less time.

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 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

Compute xbar, s2, and sfor each of the following data sets. If appropriate, specify the units in which your answer is expressed.

a.3, 1, 10, 10, 4

b.8 feet, 10 feet, 32 feet, 5 feet

c.-1, -4, -3, 1, -4, -4

d.1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce

Spreading rate of spilled liquid.A contract engineer atDuPont Corp. studied the rate at which a spilled volatileliquid will spread across a surface (Chemical EngineeringProgress, January 2005). Assume 50 gallons of methanol

spills onto a level surface outdoors. The engineer used derived empirical formulas (assuming a state of turbulent-freeconvection) to calculate the mass (in pounds) of the spillafter a period of time ranging from 0 to 60 minutes. The calculatedmass values are given in the table. Is there evidenceto indicate that the mass of the spill tends to diminish astime increases?

Support your answer with a scatterplot.

Ranking driving performance of professional golfers.Refer to The Sport Journal(Winter 2007) analysis of anew method for ranking the total driving performance ofgolfers on the PGA tour, Exercise 2.52 (p. 97). Recall thatthe method uses both the average driving distance (yards)and driving accuracy (percent of drives that land in thefairway). Data on these two variables for the top 40 PGAgolfers are saved in the accompanying file. A professionalgolfer is practicing a new swing to increase his averagedriving distance. However, he is concerned that his drivingaccuracy will be lower. Is his concern a valid one? Explain.

Consider the following sample of five measurements: 2, 1, 1, 0, 3.

a.Calculate the range, s2, and s.

b.Add 3 to each measurement and repeat part a.

c.Subtract 4 from each measurement and repeat part a.

d.Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement?

Business marketing publications.Business-to-business marketing describes the field of marketing between multiple business entities. The Journal of Business-to-Business Marketing (Vol. 15, 2008) produced a pie chart describing the number of business-to-business marketing articles published in all journals, by topical area, between 1971 and 2006. The data used to produce the pie chart are shown in the table.

Area

Number

Global Marketing

Sales Management

Buyer Behavior

Relationships

Innovation

Marketing Strategy

Channels/Distribution

Marketing Research

Services

235

494

478

498

398

280

213

131

136

Total

2,863

a.Compute the relative frequencies for the nine topical areas shown in the table. Interpret the relative frequency for Buyer Behavior.

b.Use the relative frequencies, part a, to construct a pie chart for the data. Why is the slice for Marketing Research smaller than the slice for Sales Management?

See all solutions

Recommended explanations on Math Textbooks

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