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Chapter 2: Q152SE (page 143)

U.S. business bankruptcies.The American Bankruptcy Institute and the National Bankruptcy Research Center monitor the number of business bankruptcy filings each quarter. The table below lists the number of business bankruptcy filings for each quarter of a recent 2-year period. FILING

a.Explain why the data in the table represent time series data.

b.Construct a time series plot for the quarterly number of bankruptcy filings.

c.Do you detect a trend in the time series plot? Explain.

Year

Quarter

Number of

Bankruptcies

2011

1

2

3

4

12,376

12,304

11,705

11,149

2012

1

2

3

4

10,998

10,374

9,248

9,231

Short Answer

Expert verified
  1. Data collected over a period of time is called time-series data.



C. Downward sloping trend

Step by step solution

01

Explaining why the data is a time series

Data that is spread over a period of time is called time-series data. For example, data collected every month on a person鈥檚 weight from birth to 18 years is time-series data.

The data above is a time series because the data on the number of bankruptcy filings is collected quarterly for 2 years. So the period of time over which the data is spread is 2 years.

02

Plotting the time series data

03

Detecting a trend

The most visible observation is that over a period of 2 years, the number of bankruptcy filings has declined. Therefore, there is a downward trend.

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Most popular questions from this chapter

Defects in new automobiles.Consider the following data from the automobile industry. All cars produced on a particular day were inspected for defects. The 145 defects found were categorized by type as shown in the accompanying table.

Defect Type

Number

Accessories

Body

Electrical

Engine

Transmission

50

70

10

5

10

a.Construct a Pareto diagram for the data. Use the graph to identify the most frequently observed type of defect.

b.All 70 car body defects were further classified as to type. The frequencies are provided in the following table. Form a Pareto diagram for the type of body defect. (Adding this graph to the original Pareto diagram of part a is called exploding the Pareto diagram.) Interpret the result. What type of body defect should be targeted for special attention?

Body Defect

Number

Chrome

Dents

Paint

Upholstery

Windshield

2

25

30

10

3

Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.

Calculate the range, variance, and standard deviation for the following samples:

a.39, 42, 40, 37, 41

b.100, 4, 7, 96, 80, 3, 1, 10, 2

c.100, 4, 7, 30, 80, 30, 42, 2

Consider the horizontal box plot shown below.


a.What is the median of the data set (approximately)?

b.What are the upper and lower quartiles of the data set (approximately)?

c.What is the interquartile range of the data set (approximately)?

d.Is the data set skewed to the left, skewed to the right, or symmetric?

e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?

f.Identify any outliers in the data.

Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.

a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?

b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
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