/*! 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} Q20E The article 鈥淒etermination of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q20E (page 25)

The article 鈥淒etermination of Most RepresentativeSubdivision鈥� (J. of Energy Engr., 1993: 43鈥�55) gavedata on various characteristics ofsubdivisions that couldbe used in deciding whether to provide electrical powerusing overhead lines or underground lines. Here are thevalues of the variable x=total length of streets within asubdivision:

1280

5320

4390

2100

1240

3060

4770

1050

360

3330

3380

340

1000

960

1320

530

3350

540

3870

1250

2400

960

1120

2120

450

2250

2320

2400

3150

5700

5220

500

1850

2460

5850

2700

2730

1670

100

5770

3150

1890

510

240

396

1419

2109

a. Construct a stem-and-leaf display using the thousandsdigit as the stem and the hundreds digit as theleaf, and comment on the various features of thedisplay.

b. Construct a histogram using class boundaries 0, 1000, 2000, 3000, 4000, 5000, and 6000. What proportion of subdivisions have a total length less than 2000? Between 2000 and 4000? How would you describe the shape of the histogram?

Short Answer

Expert verified

a.

The stem and leaf display is,

b.

The histogram is represented as,

Theproportion ofsubdivisions that have a total length less than 2000 is 0.489.

The proportion of subdivisions that have a total length between 2000 and 4000 is 0.489.

The shape of the histogram is right-skewed.

Step by step solution

01

Given information

Thedata on the total length of streets with a subdivisionis provided.

x represents the total length of streets within a subdivision.

02

Construct a stem and leaf display and state the features

a.

A stem-and-leaf display provides a visual representation of the dataset.

The steps to construct a stem-and-leaf display are as follows,

1) Select the leading digit for the stem and trailing digits for the leaves.

2) Represent the stem digits vertically and similarly the trailing digits corresponding to the stem digits.

3) Mention the units for the display.

The stem and leaf display for the provided scenario is,

The features that can be observed from the above display are,

1)The distribution is positively skewed.

2) There are no outliers present in the data.

03

Given information

Thedata on the total length of streets with a subdivision is provided.

x represents the total length of streets within a subdivision.

04

Construct a histogram and comment on the shape

b.

The size of the sample is 47.

The relative frequency is computed as,

\({\rm{relative frequency }} = \frac{{frequency}}{{Total\;number\;of\;observations}}\)

The table representing the relative frequency is computed as,

Class (x)

frequency

Relative frequency

0-1000

12

0.255

1000-2000

11

0.234

2000-3000

10

0.213

3000-4000

7

0.149

4000-5000

2

0.043

5000-6000

5

0.106

Steps to construct a histogram are,

1) Determine the frequency or the relative frequency.

2) Mark the class boundaries on the horizontal axis.

3) Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.

The histogram is represented as,

From the above-represented histogram, the shape of the distribution can be as positively skewed.

05

Compute the proportion

The proportion ofsubdivisions that have a total length less than 2000 is computed as,

\(\begin{aligned}P\left( {x < 2000} \right) &= 0.255 + 0.234\\ &= 0.489\end{aligned}\)

Therefore, the proportion of subdivisions that have a total length less than 2000 is 0.489.

06

Compute the proportion

The proportion ofsubdivisions that have a total length between 2000 and 4000 is computed as,

\(\begin{aligned}P\left( {2000 < x < 4000} \right) &= 0.213 + 0.149\\ &= 0.362\end{aligned}\)

Therefore, therequired proportion is 0.362

From the histogram, it can be observed that the distribution of the given data is skewed to the right.

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

Each customer making a particular Internet purchase must pay with one of three types of credit cards (think Visa, MasterCard, AmEx). Let \({{\rm{A}}_{\rm{i}}}{\rm{(i = 1,2,3)}}\) be the event that a type \({\rm{i}}\)credit card is used, with\({\rm{P}}\left( {{{\rm{A}}_{\rm{1}}}} \right){\rm{ = }}{\rm{.5}}\), \({\rm{P}}\left( {{{\rm{A}}_{\rm{2}}}} \right){\rm{ = }}{\rm{.3}}\), and\({\rm{P}}\left( {{{\rm{A}}_{\rm{3}}}} \right){\rm{ = }}{\rm{.2}}\). Suppose that the number of customers who make such a purchase on a given day is a Poisson \({\rm{rv}}\) with parameter\({\rm{\lambda }}\). Define \({\rm{rv}}\) 's \({{\rm{X}}_{{\rm{1,}}}}{{\rm{X}}_{\rm{2}}}{\rm{,}}{{\rm{X}}_{\rm{3}}}\)by \({{\rm{X}}_{\rm{i}}}{\rm{ = }}\)the number among the \({\rm{N}}\)customers who use a type \({\rm{i}}\)card\({\rm{(i = 1,2,3)}}\). Show that these three \({\rm{rv}}\) 's are independent with Poisson distributions having parameters\({\rm{.5\lambda ,}}{\rm{.3\lambda }}\), and\({\rm{.2\lambda }}\), respectively. (Hint: For non-negative integers\({{\rm{x}}_{\rm{1}}}{\rm{,}}{{\rm{x}}_{\rm{2}}}{\rm{,}}{{\rm{x}}_{\rm{3}}}\), let\({\rm{n = }}{{\rm{x}}_{\rm{1}}}{\rm{ + }}{{\rm{x}}_{\rm{2}}}{\rm{ + }}{{\rm{x}}_{\rm{3}}}\). Then\({\rm{P}}\left( {{{\rm{X}}_{\rm{1}}}{\rm{ = }}{{\rm{x}}_{\rm{1}}}} \right.\), \(\left. {{{\rm{X}}_{\rm{2}}}{\rm{ = }}{{\rm{x}}_{\rm{2}}}{\rm{,}}{{\rm{X}}_{\rm{3}}}{\rm{ = }}{{\rm{x}}_{\rm{3}}}} \right){\rm{ = P}}\left( {{{\rm{X}}_{\rm{1}}}{\rm{ = }}{{\rm{x}}_{\rm{1}}}{\rm{,}}{{\rm{X}}_{\rm{2}}}{\rm{ = }}{{\rm{x}}_{\rm{2}}}{\rm{,}}{{\rm{X}}_{\rm{3}}}{\rm{ = }}{{\rm{x}}_{\rm{3}}}{\rm{,N = n}}} \right)\) (why is this?). Now condition on\({\rm{N = n}}\), in which case the three \({\rm{Xi}}\) 's have a trinomial distribution (multinomial with three categories) with category probabilities\({\rm{.5,}}{\rm{.3}}\), and . \({\rm{2}}\).)

Exposure to microbial products, especially endotoxin, may have an impact on vulnerability to allergic diseases. The article 鈥淒ust Sampling Methods for Endotoxin鈥擜n Essential, But Underestimated Issue鈥� (Indoor Air,2006: 20鈥�27) considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the cited article.

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0

F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0

9.2 3.0 2.0 0.3

  1. Determine the sample mean for each sample. How do they compare?
  2. Determine the sample median for each sample. How do they compare? Why is the median for the urban sample so different from the mean for that sample?
  3. Calculate the trimmed mean for each sample by deleting the smallest and largest observation. What are the corresponding trimming percentages? How do the values of these trimmed means compare to the corresponding means and medians?

A sample of 77 individuals working at a particular office wasselected and the noise level (dBA) experienced by each individual was determined, yielding the followingdata (鈥淎cceptable Noise Levels for Construction Site Offices,鈥� Building Serv. Engr. Research and Technology, 2009: 87鈥�94).

55.3

55.3

55.3

55.9

55.9

55.9

55.9

56.1

56.1

56.1

56.1

56.1

56.1

56.8

56.8

57.0

57.0

57.0

57.8

57.8

57.8

57.9

57.9

57.9

58.8

58.8

58.8

59.8

59.8

59.8

62.2

62.2

63.8

63.8

63.8

63.9

63.9

63.9

64.7

64.7

64.7

65.1

65.1

65.1

65.3

65.3

65.3

65.3

67.4

67.4

67.4

67.4

68.7

68.7

68.7

68.7

69.0

70.4

70.4

71.2

71.2

71.2

73.0

73.0

73.1

73.1

74.6

74.6

74.6

74.6

79.3

79.3

79.3

79.3

83.0

83.0

83.0

Use various techniques discussed in this chapter to organize, summarize, and describe the data.

a. If a constant cis added to each \({x_i}\)in a sample, yielding \({y_i} = {x_i} + c\), how do the sample mean and median of the \({y_i}'s\)relate to the mean and median of the\({x_i}'s\)? Verify your conjectures.

b. If each \({x_i}\)is multiplied by a constant c,yielding \({y_i} = c{x_i}\), answer the question of part (a). Again, verify your conjectures.

Give one possible sample of size 4 from each of the following

populations:

a. All daily newspapers published in the United States

b. All companies listed on the New York Stock Exchange

c. All students at your college or university

d. All grade point averages of students at your college or university
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

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.