math 216 assignment 6a

Course Orientation

• Study Guide
• Computer Lab Guided Solutions (Technology Manual)
• Computer Lab Quick Review
• Self-Test B (Computer Component) Solutions

The Course of Empire, Destruction, Thomas Cole, 1836 (Wikimedia Commons, public domain)

Mathematics 216 Computer-oriented Approach to Statistics

Introduction

Welcome to Mathematics 216: Computer-oriented Approach to Statistics , a three-credit junior-level course designed to introduce and apply the basic principles of statistical analysis, including organization and presentation of statistical data, probability theory and probability distributions, estimation of population parameters from sample data, hypothesis testing, and bivariate analysis.

An important feature of Mathematics 216 is its computer component. After you have completed the exercises from the textbook, you will review and apply the statistical theory using the statistical software, an online textbook, and online computer labs. These materials will teach you how to use an industry standard statistical software application called StatCrunch to solve statistics problems.

When you have completed Mathematics 216 , you will have acquired sufficient knowledge and computer related skills to use statistics in making practical decisions and preparing reports in the workplace. As well, you will be in a much better position to competently complete papers and research projects in other university or college courses.

We cannot overestimate the value of a course that encourages you to use computer software to apply the tools of statistics in today’s society, which is increasingly dependent on electronic sources of information such as intranets, private and public online databases, the Internet, electronic instruments, and point-of-sale electronic terminals.

There are no prerequisites for Mathematics 216 ; however, students are expected to have certain skills in mathematics, including basic knowledge of high-school algebra. If you have doubts about your ability to handle the mathematics involved in this course, contact the course coordinator to discuss your situation.

This Course Orientation contains information that you will need to successfully complete Mathematics 216 . Please read it carefully before you begin this course, and refer to it as you progress through the Study Guide units.

Learning Outcomes

Upon successful completion of this course, you should be able to

• apply the basic principles of statistical analysis using a statistical software.
• employ the tools of descriptive statistics to organize, summarize and present information in a meaningful way.
• predict the likelihood of real world events, based on rules of probability and common probability distributions.
• estimate and test hypotheses regarding characteristics of both single and multiple populations.
• identify patterns of relationships between qualitative variables.
• employ linear correlation and regression methods to analyze relationships between quantitative variables.
• responsibly use statistical methods by testing the underlying assumptions.

When you have successfully completed Mathematics 216 , you will have acquired sufficient knowledge and computer related skills to utilize statistics in making practical decisions and preparing reports in the workplace. As well, you will be in a much better position to competently complete papers and research projects in other university or college courses.

Course Materials

Mathematics 216 is taught using online resources created by Athabasca University, digital web-based materials from the textbook publisher, and academic support from your tutor.

Larson, R., and Farber, B. Elementary Statistics: Picturing the World. 6th ed. Boston: Pearson, 2015.

See the e-textbook section in the Student Manual to learn about some of the features of your e-textbook, including how to download it so you can use it without being connected to the Internet—and so you can keep it after you have completed this course; print pages; search; cite passages; manage notes and highlights; and to learn about privacy issues and where to go for help.

Before you access your e-textbook, you may need to disable your pop-up blocker. If you need help doing that, follow these instructions . Then click on the e-textbook and accept the license agreement; that will give you online access to your e-textbook.

All the resources below are accessible from your course home page.

Online resources published by Athabasca University

Student Manual. Athabasca, AB: Athabasca University, 2015.

Math 216: Computer-oriented Approach to Statistics. Course Orientation. Athabasca, AB: Athabasca University, 2015.

Math 216: Computer-oriented Approach to Statistics. Study Guide. Athabasca, AB: Athabasca University, 2015.

Math 216: Computer Labs (Technology Manual). Athabasca, AB: Athabasca University, 2015.

Online resources at Pearson MyStatLab website

Pearson MyStatLab

• Student Solutions Manual
• StatCrunch statistical software (also available at statcrunch.com)
• MyStatLab Study Plan (Optional)
• Multimedia Resources (Optional)

For help accessing this resource, see MyStatLab navigation hints on the course home page.

Students enrolled in Mathematics 216 must have a scientific calculator, which is a calculator that can perform exponential operations. You may wish to use a scientific calculator that has a statistics mode to save computation time. However, you will be required to show all work on assignments and exams through substitution of appropriate values into statistical formulas. When using the calculator for computation, please do not round off any of your middle work. Round your final answers to four decimal places. Programmable calculators such as the TI-84 Plus are NOT permitted on exams.

About the Study Guide

The Study Guide is your detailed map for progressing through all the topics and activities that make up this course. Follow it closely to ensure that you do not miss key activities in this course.

The Study Guide is organized into six units, each of which is broken down into several topics that:

• Provide you with the learning objectives that you are responsible for in each section of your textbook.
• Direct you to important reading and practice exercises in your textbook.
• Direct you to solutions to practice exercises.
• Direct you to important computer problems as well as step-by-step guides to solving these problems using statistical software.

Each unit in the Study Guide closes with a unit self-test that allows you to judge your mastery of the material in that unit. The six unit self-tests help you prepare for the six assignments you will submit for evaluation and credit.

As you progress through the Study Guide, get into the habit of showing all the work you do on the assigned exercises in a notebook. Remember, on your assignments and examinations, you must always show exactly how you arrived at your answer; if your answer is incorrect, your tutor will be able to tell you exactly where you went wrong.

Course Structure

Mathematics 216 is divided into six units, covering descriptive and inferential statistics.

Unit 1. Descriptive Statistics

Designed to teach you how to organize and present statistical data in a meaningful way.

Unit 2. Probability

Introduces basic probability theory, including the addition and multiplication rules of probability, joint probability, and conditional probability.

Unit 3. Probability Distributions

Discusses probability distributions commonly used in statistics: binomial and normal probability distributions.

Unit 4. Inference on One Sample

Introduces the concepts of sampling distribution and the central limit theorem, and shows how these two important concepts are used to estimate population parameters from sample statistics. In the section on hypothesis testing, you will see how a claim regarding a characteristic of one population is made and how sample data is used to test the claim.

Unit 5. Inference on Two Samples

Presents techniques for comparing two populations using confidence intervals and tests of hypotheses.

Unit 6. Bivariate Analysis

Focuses on relationships between two variables. Correlation analysis is used to determine the strength of the relationship between two quantitative variables. Regression analysis is used to establish a mathematical formula for the relationship between two quantitative variables. The test of independence topic examines the relationship between two categorical (qualitative) variables. Analysis of variance is a technique to compare the means of three or more populations. Analysis of variance can provide valuable information on the relationship between a qualitative and quantitative variable.

Note: We strongly recommend that you follow the weekly schedule in this manual. Remember that you must complete all of the assignments before you write the final examination.

Weekly Schedule

The suggested weekly schedule below indicates the approximate amount of time you should spend on each course topic and activity. Topics to study and activities to complete are given in the Study Guide.

Although you have six months from your start date to complete the course, you will note that the schedule is based on a 22-week period. This time frame is closely in line with schedules of similar courses in traditional institutions, and allows you some leeway should an unforeseen event interrupt your studies.

You may wish to print out this Weekly Schedule. Take the time now to think about your own target calendar dates for each week and fill them in. If you find yourself falling behind, contact your tutor to discuss the situation. The course is challenging, but you should have no difficulty meeting these guidelines if you set aside consistent study periods each week and do not procrastinate.

We highly recommend that you follow the Weekly Schedule provided below.

Student Evaluation

Your final grade in Computer-oriented Approach to Statistics is based on the grades you achieve in six assignments, a mid-term examination, and a final examination.

Each assignment is worth 5% of your final grade. When you submit each assignment for marking, be sure to send both the theory and the computer components at the same time, using the same method of transmission. For each assignment, the theory component is worth 80% and the computer component 20%.

Note: The assignments are designed to challenge you. They contain only problems that you can solve using the skills and knowledge you acquired while working through the course, but you may need to combine the knowledge and skills in unexpected ways.

The mid-term examination is worth 35% of your final course grade. It will consist of a theory component worth 28% of your final course grade and a computer component worth 7% of your final course grade. The mid-term examination will be a supervised exam conducted in a manner consistent with the examination policy described in the Athabasca University calendar. The mid‑term examination will test you on the course material covered in Units 1 to 3 of the course.

The final examination is worth 35% of your final course grade. It will consist of a theory component worth 28% of your final course grade and a computer component worth 7% of your final course grade. The final examination will be a supervised exam conducted in a manner consistent with the examination policy described in the Athabasca University calendar. The final examination will test you on the course material covered in Units 4 to 6 of the course.

In total, the theory section of the course makes up 80% of your composite course grade and the computer-related questions and assignments contribute 20% to your composite grade.

To pass this course, you must achieve a mark of at least 50% on each of the following:

• the theory component of the mid-term examination
• the computer component of the mid-term examination
• the theory component of the final examination
• the computer component of the final examination.

Your composite course grade must also be at least 50% for you to pass this course. Note: Students who do not achieve a minimum passing grade of 50% on any examination theory or computer component will be allowed to write one supplemental for each examination component.

You may wish to use the table below to keep a record of your performance in this course:

Examination Materials

The mid-term examination will cover Units 1 to 3. The final examination will cover Units 4 to 6.

Note: In both the mid-term and the final examination you are allowed to bring in ONE 8½ × 11 inch summary sheet that can include anything you feel may help you complete the exam successfully. The summary sheet may contain formulas and worked-out examples. You may use both sides of this summary sheet.

No books or notes may be brought into the exam other than the double-sided summary sheet noted above. For security reasons, your summary sheet MUST be handed in with your completed exam. Therefore, you may wish to make a copy in case you are required to, or decide to, write a supplemental examination.

You are expected to use a standard scientific calculator in each exam. Programmable calculators, graphing calculators (such as the TI 83 or TI 84 Plus etc.), computers or other mobile devices,  are not allowed into the exam room.

To study for each exam, we suggest the practices below. (We will use the mid‑term as an example.)

• For each topic in Units 1 to 3 of the Study Guide, review each Learning Objective along with the work you have shown when completing each exercise you were assigned in the related section.
• Re-do the self-tests for Units 1 to 3.
• Re-do the assignments for Units 1 to 3.

Follow the same approach when studying for the final exam.

Getting Off to the Right Start

We suggest the following steps when working through this course.

• Read through this entire Course Orientation and briefly review the course materials.
• Before you begin any unit of the Study Guide, check the Weekly Schedule in the Course Orientation. Be sure you have identified weekly dates so that you can pace yourself appropriately through this course.
• In the Study Guide, scan the Contents column of Unit 1, and read the Introduction to Unit 1.
• Review key learning objectives related to this topic.
• Read the specified pages in your textbook.
• Work through the Try It Yourself exercises related to Unit 1.

Work through the suggested exercises in the textbook in Unit 1.

Note: The most important activity in this course is the completion of the suggested exercises in the Study Guide units. We encourage you to show your work when completing each exercise and keep all your work in a notebook. This practice will help you prepare for your assignments and exams.

• The Study Guide will direct you to complete a few more topics in Unit 1.
• Next is Computer Lab 1A, several activities to complete using the statistical software StatCrunch.
• After you complete the remaining topics in Unit 1, work through Self-test 1. Again, be sure to show all your work when completing the self‑test.
• Complete the assignment and submit it to your tutor for grading. Be sure to keep a backup copy of the submitted assignment.
• Follow Steps 2 to 8 above for each unit of this course.

Mathematics (MATH) 216

Delivery mode:

Individualized study online with eText

Area of study:

Prerequisites:

None. Fundamental mathematical skills are required, particularly the ability to do basic algebra. Reviews of basic mathematics are available at Athabasca University Library. MATH 101  (a non-credit course) is suitable preparation for taking MATH 216, for those students concerned about their mathematical background. Familiarity with the Windows operating system is essential.

Course start date:

If you are a:

• Self-funded student: register by the 10th of the month, start on the 1st of the next.
• Funded student: please check the next enrolment deadline and course start date .

MGSC 301 , MATH 215 . (MATH 216 may not be taken for credit if credit has already been obtained for MGSC 301 or MATH 215.)

MATH 216 is not available for challenge.

Faculty of Science and Technology

Both the midterm and final are closed-book, machine-marked exams in the Möbius online platform and are invigilated through ProctorU . See the Evaluation section of the syllabus for more information.

Mathematics Diagnostic Assessment . This online test contains 70 questions that will help you assess your mathematical skills. Based on your score, we will recommend which Athabasca University mathematics course you are likely ready to take successfully.

The web-based statistical software used in MATH 216 is compatible with the following operating systems: Windows 10, 8.1. 8, and 7; Mac OS 10.12 – Sierra, 10.11 - El Capitan, 10.10 – Yosemite.

Learning outcomes

Important links.

MATH 216 gives students a working knowledge and understanding of descriptive and inferential statistics and how statistics is applied in the sciences, social sciences, and business. An important feature of MATH 216 is its computer component, which teaches you how to use an industry standard statistical software application to apply the tools of statistics to make practical decisions, prepare reports in the workplace, and effectively complete papers and research projects in other university courses. We cannot underestimate the value of a course which encourages you to use computer software to apply the methods of statistics, in a society which is increasingly dependent on electronic sources of information such as intranet databases, external databases, the internet, electronic instruments, and point of sales electronic terminals. MATH 216 is a multimedia course designed to appeal to a wide range of students with diverse learning styles.

• Unit 1: Descriptive Statistics
• Unit 2: Probability
• Unit 3: Probability Distributions
• Unit 4: Inference on One Sample
• Unit 5: Inference on Two Samples
• Unit 6: Bivariate Analysis

Upon successful completion of this course, you should be able to

• apply the basic principles of statistical analysis using statistical software.
• employ the tools of descriptive statistics to organize, summarize, and present information in a meaningful way.
• predict the likelihood of real-world events, based on rules of probability and common probability distributions.
• estimate and test hypotheses regarding characteristics of both single and multiple populations.
• identify patterns of relationships between qualitative variables.
• employ linear correlation and regression methods to analyze relationships between quantitative variables.
• responsibly use statistical methods by testing the underlying assumptions.

To receive credit for MATH 216, you must achieve a mark of at least 50 percent on both the midterm and final examinations, and y our composite course grade must be at least  D (50 percent) .

The midterm and final are closed-book, machine-marked exams in the Möbius online platform and are invigilated through   ProctorU . Your exams must be requested in advance, and you must pay the ProctorU invigilation fees. You will have three (3) hours to complete each exam.

Note: You are expected to use a standard scientific calculator in each exam. Programmable calculators, graphing calculators (such as the TI83, etc.), computers, or any other mobile electronic devices may not used during the exams.

The weighting of the composite course grade is as follows:

To learn more about assignments and examinations, please refer to Athabasca University’s online Calendar .

Larson, R., & Farber, B. (2019).  Elementary statistics: Picturing the world  (7th ed.). Pearson. (eText)

Registration in this course includes an electronic textbook. For more information on electronic textbooks , please refer to our eText Initiative site .

Online Resources at Pearson MyLab Website

• Student's Solutions Manual
• StatCrunch statistical software (also available at statcrunch.com)
• MyLab Study Plan (Optional)
• Multimedia Resources (Optional)
• Academic advising
• Program planning
• Request assistance
• Support services

Athabasca University reserves the right to amend course outlines occasionally and without notice. Courses offered by other delivery methods may vary from their individualized study counterparts.

Opened in Revision 4, June 10, 2020

Updated January 16, 2024

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• MATH 216 Assignment3B

Statisticstaker

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• Course Orientation
• Study Guide
• Computer Lab Guided Solutions (Technology Manual)
• Computer Lab Quick Review
• Self-Test B (Computer Component) Solutions

Mathematics 216 Computer-oriented Approach to Statistics

Computer Lab 1B with Guided Solutions ( Technology Manual )

With the aid of the Guided solution, use StatCrunch to work through each of the following Activities that relate to Chapter 2 in your eText.

Activity 1. Construct a frequency distribution with classes.

Task 1. example 1 from elementary statistics , 6th edition.

Example 1 Constructing a Frequency Distribution from a Data Set

Here, you will open the StatCrunch data file GPS.txt from the AU Math216 2020 group folder on the StatCrunch website and construct a frequency distribution. The lower limit of the first class is 65 and the bin width (width of each class) is 40.

Figure 1. Frequency table for GPS price.

Guided Solution 1a

Open the StatCrunch Data File GPS.txt

• Open your web browser.
• Go to the website www.statcrunch.com .
• Sign in with your Pearson MyLab user id and password. This should take you to the StatCrunch home page.
• Click the menu option Groups .
• In the Search box, type the group name “AU Math216 2020”, and hit the Enter key.
• In the next window that displays, click the AU Math216 2020 link.
• In the next window, in the Search box, type GPS to bring up the GPS.txt file link.
• Click on the GPS.txt link to open the GPS data file.

Guided Solution 1b

Create a Bins(Classes) Column as the second column in the data table.

Here, you will create a bins column consisting of the 7 classes shown in the first column of Figure 1 above. For each of these classes, the lower boundary is included as the class, but the upper boundary is not included in that same class.

• Click the menu option sequence Data → Bin .
• Select the variable GPS Prices in the Select Column box.
• In the Define Bins section, select Use fixed width bins . Type 65 in the Start at box. Type 40 in the Binwidth box.

In the Bin edges section, select Include left end point. See Figure 2.

Figure 2. Bin column window.

Click Compute . This will display the Bins column as the second column in the GPS.txt Data Table. See Figure 3 below.

Figure 3. First 10 rows of the GPS.txt data sheet

Guided Solution 1c

Create a frequency table for GPS prices.

Here, you will create the frequency table displayed in Figure 1 above, with the bins column as the first column and other columns for frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies.

• Click Stat → Tables → Frequency.
• Click the variable Bin (GPS Prices (in dollars)). This variable will show in the box to the right.

In the Statistics box, hold the Ctrl key down while you click Frequency, Relative Frequency, Cumulative Frequency, Cumulative Relative Frequency. See Figure 4.

Figure 4. Creating the frequency table for GPS prices.

• Click Compute. This will create the frequency table shown in Figure 1 above.

Guided Solution 1d

Copy the frequency table into a word processing file named ComputerLab1B.

Here, you will open a new word processing file and call it ComputerLab1B; copy and paste the frequency table created in StatCrunch into this blank file; and save this file as ComputerLab1B on your hard drive or personal storage space on the cloud.

• For help with copying StatCrunch data, see Copying Materials from StatCrunch . Hint: In the StatCrunch frequency table, click Ctrl+A, Ctrl+C. In the word processing software, click Ctrl+V.
• Save your Word file as ComputerLab1B. Note that you will NOT be asked to send this file to your tutor.
• You may wish to create a folder called Math 216 and save ComputerLab1B inside it, as you will later be asked to save other solutions in the ComputerLab1B file.

Task 2. Interpretation - Example 1

Insert the questions below into your ComputerLab1B word processing file, under the frequency table you just pasted.

Based on your review of the pasted frequency table, type your answers to these questions in the solutions spaces provided. (If you need help answering these questions, see the Solutions section that follows them.)

The most common price range (class) for the GPS navigators is from $_____ to $_____

What percentage of the 30 GPS navigators sampled were in the most common price range?

How many GPS navigators sold at a price below $145?

What percentage of the 30 GPS navigators sampled sold at less than $185?

Remember to resave your file under the file name ComputerLab1B.

Solutions to Task 2

• $105 to $145 (9 in the Frequency column)
• 30% (0.3 in the Relative Frequency column)
• 15 navigators (15 in the Cumulative Frequency column)
• 70% (0.7 in the Cumulative Relative Frequency column)

Task 3. Exercise 29 from Elementary Statistics , 6th edition

Exercise 29. Political Blog Reading Times

In Exercise 29 construct a frequency distribution for the data set using the indicated number of classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency?

Here, you will open the StatCrunch data file Ex2_1-29.txt from the AU Math216 2020 group folder on the StatCrunch website and construct a frequency distribution, following the guided solutions. The lower limit of the first class starts with 0, and the bin width is 8 (which implies that the first class is from 0 to 8 but does not include 8).

Figure 5. Frequency Table for Political Blog Reading Times

Guided Solution 3a

Open the StatCrunch Data File Ex2_1-29.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 3b

Create a Bins(Classes) Column as the Second Column in the Data Table.

Here, you will create a bins column consisting of the 5 classes shown in the first column of Figure 5 above. For each of these classes, the lower boundary is included as the class, but the upper boundary is not included in that same class.

• Click the menu option sequence Data → Bin.
• In the Select Column box, select the variable Minutes reading political blog.
• In the Define Bins section, select Use fixed width bins. Type 0 in the Start at box. Type 8 in the Binwidth box.
• In the Bin edges section, select Include left endpoint.
• Click Compute. This will create the Bins column as the second column in the Data Table.

Guided Solution 3c

Create a frequency table for Minutes Reading Political Blog.

Here, you will create the frequency table displayed in Figure 5 above, with the bins column as the first column and other columns for frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies.

• Click the menu option sequence Stat → Tables → Frequency .
• Click the variable Bin (Minutes reading political blog); this will display it in the box to the right.
• In the Statistics box, hold the Ctrl key down while clicking on Frequency, Relative Frequency, Cumulative Frequency, and Cumulative Relative Frequency.
• Click Compute. This will create the frequency table shown in Figure 5 above.

Guided Solution 3d

Copy the frequency table into your word processing file ComputerLab1B.

Here, you will open the word processing file that you named ComputerLab1B, and copy and paste the updated frequency table into it, after the last items that you pasted in the previous exercise.

• For help with copying StatCrunch data, see Copying Materials from StatCrunch .
• Save this file as ComputerLab1B on your hard drive or personal storage space on the cloud.

Task 4. Interpretation - Exercise 29

How many individuals spent between 8 and 16 minutes per day reading political blogs?

What percentage of the individuals sampled, tend to read political blogs between 0 to 8 minutes per day?

How many individuals spent less than 16 minutes each day reading political blogs?

What percentage of the individuals sampled spent less than 24 minutes each day reading political blogs?

Remember to save your work under the same file name: ComputerLab1B.

Solutions to Task 4

• 8 people—see the 8 in the Frequency column in table.
• 32%—see the .32 in the Relative Frequency column
• 16 people—see the 16 in the Cumulative Frequency column
• 76%—see the .76 in the Cumulative Relative Frequency column

Task 5. Exercise 31 from Elementary Statistics , 6th edition

You will open the StatCrunch data file Ex2_1-31.txt from the AU Math216 2020 group folder on the StatCrunch website and construct a frequency distribution, following the guided solutions below. The lower limit of the first class is 1000 and the bin width is 1020 (which implies that the first class is from 1000 to 2020 but does not include 2020).

Figure 6. Frequency Table for July sales

Guided Solution 5a

Exercise 31. July Sales

Open the StatCrunch Data File Ex2_1-31.txt from the AU Math216 2020 group folder on the StatCrunch website. You will see July sales as the first column in the data file.

Guided Solution 5b

Create a Bins(Classes) Column as the second column in the data table. Here, you will create a bins column consisting of the 5 classes shown in the first column of Figure 6 above. For each class, the lower boundary is included as the class, but the upper boundary is not included in that same class.

• Select the column July sales.
• In Define bins, start at 1000; use Binwidth of 1020.

Guided Solution 5c

Create a frequency table for July sales.

Here, you will create the frequency table displayed in Figure 6 above, with the bins column as the first column and the other columns displaying frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies.

• Select the column Bin (July sales).

Guided Solution 5d

Copy the frequency table into a word processing file

• In the word processing file ComputerLab1B, type Exercise 31 page 52 below the bottom item.
• Save your file, ComputerLab1B.

Task 6. Interpretation - Exercise 31

What monthly sales range (class) occurred most frequently in July?

What percentage of the sales representatives earned between $3040 and $4060 in sales in July?

How many sales representatives earned less than $3040 per month in July?

What percentage of the sales representatives earned less than $4060 in July?

Remember to save your work as ComputerLab1B.

Solutions to Task 6

• $1,000 to $2,020 (12 in the Frequency column in table)
• 9.09% (.0909 in the Relative Frequency column)
• 15 sales representatives (15 in the Cumulative Frequency column)
• 77% (.7727 in the Cumulative Relative Frequency column)

Activity 2. Construct a frequency histogram.

Task 7. example 3 from elementary statistics , 6th edition.

Here, you will open the StatCrunch data file GPS.txt from the AU Math216 2020 group folder on the StatCrunch website and construct a frequency histogram, labeled with class boundaries, following the guided solutions below. The lower limit of the first class starts with 64.5 and the bin width (width of each class) is 40. Your graph should look like Figure 7.

Figure 7. Frequency Histogram for GPS Prices

Guided Solution 7a

Open the StatCrunch Data File GPS.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 7b

Using StatCrunch, create a frequency histogram for GPS Prices.

You will create the frequency histogram displayed in Figure 7 above, with the bins starting at 64.5 and a bin width of 40.

• Click the menu option sequence Graph → Histogram.
• In the Select Column box, select the variable GPS prices (in dollars); it will display in the box to the right.
• In the Type box, select Frequency.
• In the Bins section, type 64.5 in the Start at box and 40 in the width box (see Figure 8).
• Select the Display option: Value above bar
• Click Compute to display the frequency histogram shown in Figure 7 above.

Figure 8. Histogram window.

Guided Solution 7c

Copy the frequency histogram into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Example 3 page 44 below the bottom item.
• Save your Word file, ComputerLab1B.

Task 8. Exercise 31 from Elementary Statistics , 6th edition

Here, you will open the StatCrunch data file Ex2_1-31.txt from the AU Math216 2020 group folder on the StatCrunch website and construct a frequency histogram, following the guided solutions below. The lower limit of the first class is 999.5 and the bin width is 1020.

Figure 9. Frequency histogram for July sales.

Guided Solution 8a

Open the StatCrunch Data File Ex2_1-31.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 8b

Create a Frequency Histogram for July Sales.

Here, you will create the frequency histogram displayed in Figure 9 above, with the bins starting at 999.5 and having a bin width of 1020.

• In the Select column box, select the variable July sales.
• In the Bins section, type 999.5 in the Start at box, and type 1020 in the Width box.
• Select the Display option: Value above bar.
• Click Compute to display the frequency histogram.

Guided Solution 8c

Copy the Frequency Histogram into a word processing file ComputerLab1B.

• Open the ComputerLab1B word processing file and, below the bottom item, type Exercise 31 page 52.

Activity 3. Construct a relative frequency histogram.

Task 9. example 5 from elementary statistics , 6th edition.

Here, you will open the StatCrunch data file GPS.txt and construct a relative histogram, labeled with class boundaries, following the guided solutions below. The lower limit of the first class is 64.5 and the bin width (width of each class) is 40. Your graph should look like Figure 11.

Figure 10. Relative Frequency Histogram for GPS Prices

Guided Solution 9a

Guided solution 9b.

Create a relative frequency histogram for GPS prices.

Here, you will create a relative frequency histogram displayed in Figure 10 above, with the bins starting at 64.5 and a bin width of 40.

• in the Select column box, select the variable GPS prices (in dollars).
• In the Type box, select Relative Frequency.
• In the Bins section, type 64.5 in the Start box and 40 in the Width box.
• Select the Display option: Value above bar. See Figure 11.

Figure 11. Histogram window.

• Click Compute to display the histogram shown in Figure 10.

Guided Solution 9c

Copy the relative frequency histogram into the Word file ComputerLab1B.

Task 10. Exercise 35 from Elementary Statistics , 6th edition

Exercise 35. Taste Test

Here, you will open the StatCrunch data file Ex2_1-35.txt and construct a relative histogram, labeled with class boundaries, following the guided solutions below. The lower limit of the first class is .5 and the bin width is 2. Your graph should look like Figure 12.

Figure 12. Relative Frequency Histogram for Taste Test Ratings

Guided Solution 10a

Open the StatCrunch Data File Ex2_1-35.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 10b

Create a relative frequency histogram for Ratings. Here, you will create a relative frequency histogram displayed in Figure 12 above, with the bins starting at .5 and having a bin width of 2.

• In the Select Column box, select the variable Ratings.
• In the Bins section, type .5 in the Start box and 2 in the Width box.
• Click Compute to display the histogram as in Figure 12.

Guided Solution 10c

• Open the word processing file ComputerLab1B, and type Exercise 35 page 52 below the bottom item.

Activity 4. Construct a frequency polygon.

Task 11. example 4 from elementary statistics , 6th edition.

Here, you will open the StatCrunch data file GPS.txt and construct a frequency polygon, following the guided solutions below. Your graph should look like Figure 13.

Figure 13. Frequency POLYGON for GPS Prices

In constructing the frequency polygon, you will use StatCrunch to plot the midpoint of each class, defined by upper and lower class boundaries, against the class frequency.

Guided Solution 11a

Guided solution 11b.

• In the Select Column box, select the variable GPS Prices (in dollars).
• In the Define Bins section, select Use fixed width bins. Type 64.5 in the Start box; type 40 in the Binwidth box.
•  In the Bin edges section, select Include left endpoint.

Click Compute to display the Bins column as the second column. Figure 14 shows the first two rows of the data table.

Figure 14. Bin column displays the class boundaries related to each GPS price.

Guided Solution 11c

Recode the boundaries for each class with the class midpoint value, and display in the third column in the data table.

Here, you will display a class midpoint value beside each class in the Bin Column.

• Click the menu option sequence Data → Recode.
• In the Select Column section, click Bin(GPS Prices (in dollars)).
• Click Compute to display a table showing the original Bins column and the recoded column that you want to create.

In the Recoded column, calculate and type the class midpoint values (as shown in Figure 15) as the values to be inserted in the Recode column.

Figure 15. Typing class midpoints in the Recoded column.

• Click Compute to create a new column, Recode(Bin(GPS prices (in dollars))), which displays the midpoint of each class in the data table.

Guided Solution 11d

Create a frequency table, with the first column showing the recoded values (class midpoints), and the second column showing the related frequencies.

• Click the menu option sequence Stat → Tables → Frequency.
• In the Select Columns box, click Recode(Bin(GPS prices (in dollars))) as the variable.
• In the Statistics box, select Frequency.
• In the Output section, select Store output in data table.

Click Compute. This displays two new columns in the data table, shown in Figure 16.

Figure 16. Two new variables in data table: recode (showing class midpoints) and frequency.

Guided Solution 11e

Create a scatter plot graph, with the recode values being the x -values and the frequency values being the y -values.

• Click the menu option sequence Graph → Scatter Plot.
• Select the Recode(Bin(GPS prices (in dollars))) as the x  column variable.
• Select Frequency as the y column variable.
• In the Display box, select Lines.
• Click Compute to display the Frequency polygon, as shown in Figure 13 above.

Guided Solution 11f

Paste the Frequency Polygon into word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B and, below the bottom item, type Example 4 page 45.
• Save your Word file , ComputerLab1B.

Task 12. Interpretation - Example 4 page 45

Insert the question below into your ComputerLab1B word processing file, under the frequency table you just pasted.

Based on your review of the pasted polygon, type your answer to this question in the solution space provided. (If you need help answering the question, see the Solution that follows.)

Is the distribution of navigator prices positively or negatively skewed? Interpret your answer.

Solution to Task 12

• The navigator prices are positively skewed. This means that, while there are a few non-typical high prices, most of the prices are in the lower price ranges.

Activity 5. Construct a pie chart to analyze qualitative survey data.

In Computer Lab 1, you created the data file STAT101 Survey Responses and saved it in your My Data Folder on the StatCrunch website. This data file contains the responses from twenty students to the two questions “What is your gender?” and “What final course grade do you expect?”

Task 13. Create a pie chart.

Here, you will open the data file STAT101 Survey Responses from your My Data Folder and create a pie chart describing the relative frequencies of the two genders in the survey sample.

Guided Solution 13a

Open the Stat101 Survey Responses data file from your My Data Folder on the StatCrunch website.

• In your web browser, go to www.StatCrunch.com and sign in.
• Click the menu option MyStatCrunch. Click the My Data link.

Click STAT101 Survey Responses. This will open the STAT101 data in the data table, with 20 data entries displayed for the two variables Gender and Grade. Figure 17 shows the first three rows.

Figure 17. First three rows of the Stat101 Survey Responses data file.

Guided Solution 13b

Recode the Gender variable values.

Before conducting statistical analysis involving qualitative variables such as Gender, it is appropriate to recode the M  value to display as Male and the F  value as Female. This makes it easier to understand the statistical analysis graphs and tables. Here, you will use StatCrunch to do this recoding.

• With theStat101 data file open, Click the menu option sequence Data → Recode.
• click Gender in the Select Column section
• Click Compute. This will display a table with the Original column and a Recode column

Edit the Recode column to show Female as the first value and Male as the second value. See Figure 18.

Figure 18. Recoding the Gender variable.

• Click Compute. This will show the data table with a new Recode (Gender) column with 20 recoded values.

Guided Solution 13c

Create a pie chart showing the Relative Frequencies for the Recoded Gender Values.

• With theStat101 data table open, click the menu option sequence Graph → Pie Chart → With Data.
• In the Select Column section, click Recode(Gender).
• In the Display box, click Percent of Total.

Click Compute to create the pie chart as shown in Figure 19.

Figure 19. Pie chart: Relative Frequencies for Gender Values

Guided Solution 13d

Copy the pie chart into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Pie Chart for Gender below the bottom item.

Task 14. Interpretation - Pie Chart for Gender for Stat101 Survey Responses Data File

Insert the question below into your ComputerLab1B word processing file, under the pie chart you just pasted.

Based on your review of the pasted pie chart, type your answer to this question in the solution space provided. (If you need help answering the question, see the Solution that follows.)

What is the most frequent gender in the Stat101 survey sample?

Solution to Task 14

• The predominant gender is male, with only 40% of the sample being females and 60% males.

Activity 6. Construct a Pareto chart for qualitative data.

Task 15. construct a pareto chart for qualitative data..

Here, you will construct a Pareto chart, which is a vertical bar chart. Bar height will reflect the frequency of the data value. The bars are in order of decreasing height, with the tallest bar on the left.

Guided Solution 15a

Create a StatCrunch data file based on the data in Figure 20 below.

Figure 20 shows the results of a survey of 55 employees working in a large car dealership. The survey asked employees to identify their favourite day of the week. The results are summarized in the form of a completed frequency distribution in Figure 20.

Figure 20. Results of care dealership survey.

• Open StatCrunch with a blank data table.
• Type Day as the first variable (column) name and Frequency as the second variable (column) name.
• Enter all the data values and their frequencies as shown in Figure 20.
• Click Data → Save.
• Type the filename FavouriteWeekday.
• Click the Save button to save to your My Data folder. Keep this data table displayed for Guided Solution 15b.

Guided Solution 15b

Create a Pareto chart for the data in the FavouriteWeekday data file.

• With the FavouriteWeekday data file open, click the menu option sequence Graph → Bar Plot → With Summary.
• in the Categories in box, select the variable Day.
• In the Counts in box, select the variable Frequency.
• In the Order by box, select Count Descending.

Under Display, select Value above bar. See Figure 21.

Figure 21. Options for Frequency Pareto Chart

Click Compute to display the Pareto chart as shown in Figure 22.

Figure 22. Pareto chart for FavouriteWeekday.

Guided Solution 15c

Copy the Pareto chart into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Pareto Chart for FavouriteWeekday Data File below the bottom item.

Task 16. Interpretation - Pareto Chart for FavouriteWeekday data file

Insert the question below into your ComputerLab1B word processing file, under the Pareto chart you just pasted.

Based on your review of the pasted Pareto chart, type your answer to this question in the solution space provided. (If you need help answering the question, see the Solution that follows.)

What are the top three favourite weekdays of the car dealership employees?

Solution to Task 16

• Top three favourite days are: Saturday, Friday, and Sunday.

Activity 7. Construct a stem-and-leaf plot for quantitative data.

Task 17. exercise 21 from elementary statistics , 6th edition.

Exercise 21. Highest Paid CEOs

Here, you will open the StatCrunch data file Ex2_2-21.txt and construct a stem-and-leaf plot following the guided solutions below.

Figure 23. Stem-and-leaf plot for ages of highest-paid CEOs.

Guided Solution 17a

Open the StatCrunch Data File Ex2_2-21.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 17b

Create a stem-and-leaf plot for the Ex2_2-21.txt data file.

• With your the data file Ex2_2-21.txt open, click the menu option sequence Graph → Stem and Leaf
• In the Select Columns box, select the variable Ages.
• In the Leaf Unit box, select 1.
• In the Outlier Trimming box, select None.
• Click Compute to display the stem-and-leaf plot for Ages as shown in Figure 25 above.

Guided Solution 17c

Copy the stem-and-leaf plot into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Stem-and-leaf Plot for Ages of Highest-paid CEOs below the bottom item.
• With your cursor in the stem-and-leaf window, click Ctrl+A to select the entire stem-and-leaf plot.
• With your cursor in your Word file below the heading Stem-and-leaf Plot for Ages of Highest-paid CEOs, click Paste or Ctrl+V to paste the plot into the file.

Task 18. Interpretation - Stem-and-leaf plot for Ages of Highest Paid CEOs

Insert the question below into your ComputerLab1B word processing file, under the stem-and-leaf plot you just pasted.

Based on your review of the pasted stem-and-leaf plot, type your answer to this question in the solution space provided. (If you need help answering the question, see the Solution that follows.)

How many CEOs are in their fifties? What percentage of all CEOs surveyed are in their fifties?

Solution to Task 18

• 18 CEOs or (18/30) = .60 or 60% of those surveyed.

Activity 8. Work with measures of central tendency: mean, median, mode.

Task 19. try it yourself 2 from elementary statistics , 6th edition.

Open the StatCrunch data file TIY2_3-2.txt and compute the mean, median, and mode of the ages of 25 rock fans, following the guided solutions below.

Figure 24 describes the StatCrunch output for these three measures of central tendency in table form.

Figure 24. Summary Statistics table: Mean, median, mode ages of rock fans.

Guided Solution 19a

Open the StatCrunch data file TIY2_3-2.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 19b

Compute the mean, median, and mode for ages of fans.

Here, you will create the Mean, Median, and Mode table shown in Figure 24 above.

• Click the menu option sequence Stat → Summary Stats → Columns
• In the Select Column box, click the variable Ages of fans.

In the Statistics box, hold the Crtl key down while clicking on Mean, Median, and Mode to select these measures. See Figure 25.

Figure 25. Summary Stats window.

• Click Compute to display the Mean, Median, and Mode table as shown in Figure 24 above.

Guided Solution 19c

Copy the Summary statistics table into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Mean, Median, Mode for Ages of Fans below the bottom item.

Task 20. Interpretation - Summary Statistics Table on Mode, Median, and Mean

Insert the questions below into your ComputerLab1B word processing file, under the Summary statistics table you just pasted.

Based on your review of the pasted Summary statistics table, type your answers to these questions in the solutions spaces provided. (If you need help answering these questions, see the Solutions section that follows them.)

What is the most frequently occurring age in this sample?

What is the middle age in this sample?

What measure is based on a calculation involving all 25 age values?

Is the sample of 25 ages positively or negatively skewed? Explain.

Solutions to Task 20

• Solution: Mode = 21
• Solution: Median = 24
• Solution: Mean = 25.6
• Solution: As the mean exceeds the median, the data is positively skewed.

Activity 9. Work with measures of variation: range, standard deviation, variance

Task 21. exercise 15 from elementary statistics , 6th edition.

Open the StatCrunch data file Ex2_4‑15.txt and compute the range, standard deviation, variance of the ages of 20 clothing shoppers, following the guided solutions below.

Exercise 15. Age of Shoppers

Figure 26 describes the StatCrunch output for these three measures of variation in table form.

Figure 26. Range, standard deviation, variance of the ages of clothing shoppers.

Guided Solution 21a

Open the StatCrunch Data File Ex2_4-15.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 21b

Compute the range, standard deviation, variance for a sample of ages of clothing shoppers.

Here, you will create the Range, Standard Deviation, Variance table displayed in Figure 28 above.

• Click the menu option sequence Stat → Summary Stats → Columns.
• In the Select Columns box, click the variable Ages (in years).

In the Statistics box, hold the Crtl key down while clicking Range, Std. dev., and Variance to select these measures. See Figure 27.

Figure 27. Summary Stats window.

• Click Compute to display the Range, Std. dev., and Variance table as shown in Figure 26.

Guided Solution 21c

• Open the word processing file ComputerLab1B, and type Range, Std. dev., Variance for Ages of Clothing Shoppers below the bottom item.
• With your cursor in the Summary statistics table, click Ctrl+A to select the entire table. Then click Ctrl+C to copy the statistics.
• With your cursor in your Word file below the heading Range, Std. dev., Variance for Ages of Clothing Shoppers, click Paste or Ctrl+V to paste the table into the file.

Task 22. Interpretation - Summary Stats Table on Range, St. dev., Variance

Insert the question below into your ComputerLab1B word processing file, under the Summary Stats table you just pasted.

Based on your review of the pasted table, type your answer to this question in the solution space provided. (If you need help answering the question, see the Solution that follows.)

In this sample of shoppers, the typical shopper’s age is approximately ________ years above or below the mean age of 17 years age.

Solution to Task 22

• In this sample of shoppers, the typical shopper’s age is approximately 2.59 years (standard deviation) above or below the mean age of 17 years age.

Activity 10. Work with measures of position: Q 1, Q 2, Q 3, Interquartile Range.

Task 23. example 2 from elementary statistics , 6th edition.

Open the StatCrunch data file Tuition.txt and compute the First, Second, and Third Quartiles, and the Interquartile Range for the tuition costs (in thousands of dollars) for 25 colleges, following the guided solutions below.

Example 2 Tuition Costs

Figure 28 shows the StatCrunch output for these four measures of position in table form.

Figure 28. Q 1, Q 2 (median), Q 3, interquartile range for College tuition costs.

Guided Solution 23a

Open the StatCrunch Data File Tuition.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 23b

Compute the Q 1, Q 2 (median), Q 3, Interquartile Range for College Tuition Costs.

Here, you will create the Summary statistics table displayed in Figure 28 above.

• In the Select Columns box, click the variable Tuition costs (in thousands of dollars) to select it.

In the Statistics box, hold the Crtl key down while clicking Q 1, Median, Q 2, and IQR to select these measures. See Figure 29.

Figure 29. Summary Stats Window

• Click Compute to display the Summary statistics table shown in Figure 28 above.

Guided Solution 23c

• Open the word processing file ComputerLab1B, and type Q 1, Q 2, Q 3, and Interquartile Range for College Tuition Costs below the bottom item.

Task 24. Interpretation of Summary Statistics table on Q 1, Q 2, Q 3, Interquartile Range

Based on your review of the pasted table, type your answers to these questions in the solutions spaces provided. (If you need help answering these questions, see the Solutions section that follows them.)

Approximately 25% of the colleges surveyed charge a tuition of $________ or less, and about half of the colleges charge a tuition of $________ or less.

Approximately 25% of the colleges surveyed charge a tuition of $________ or more.

The tuition costs of the colleges that fall in the middle 50% of college tuition costs vary by, at most, $________.

Solutions to Task 24

• Approximately 25% of the colleges surveyed charge a tuition of $27,000 ( Q 1) or less, and about half of the colleges charge a tuition of $32,000 (median) or less.
• Approximately 25% of the colleges surveyed charge a tuition of $40,000 ( Q 3) or more.
• The tuition costs of the colleges that fall in the middle 50% of college tuition costs vary by, at most, $13,000 ( Q 3– Q 1).

Activity 11. Construct a box-and-whisker plot for quantitative data.

Task 25. exercise 25 from elementary statistics , 6th edition.

Open the StatCrunch data file Ex2_5-25.txt and create a box-and-whisker plot for the number of hours TV watched per day by a sample of 28 people, following the guided solutions below.

Exercise 25. TV Viewing

Figure 30 shows the StatCrunch box-and-whisker plot. Construct this plot and use it to quickly determine 6 measures for number of hours of TV watched per day: minimum, maximum, Q 1, Q 2, Q 3, and IQR .

Figure 30. Box-and-whisker plot for hours of TV watched per day.

Guided Solution 25a

Open the StatCrunch data file Ex2_5-25.txt from the AU Math216 2020 group folder on the StatCrunch website.

Guided Solution 25b

Create a box-and-whisker plot for hours of TV watched per day.

• Click the menu option sequence Graph → Boxplot.
• In the Select Columns box, click the variable Hours of TV watched.
• In the Other options section, click Draw boxes horizontally, to ensure that the plot is aligned horizontally.

In the Graph properties section, in the box X -axis label, type Hours of TV Watched Per Day. See Figure 31.

Figure 31. Boxplot window.

• Click Compute to display the box-and-whisker plot shown in Figure 30 above.

Guided Solution 25c

Copy the box-and-whisker plot into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Box-and-whisker Plot for Hours of TV Watched Per Day below the bottom item.

Task 26. Interpretation of the Box-and-whisker Plot

• With the box-and-whisker plot displayed in the Boxplot window in StatCrunch, quickly determine the six measures for Hours of TV Watched per Day: Minimum, Maximum, Q 1, Q 2, Q 3, and IQR . Note the Guided solution below.

Guided Solution 26

Based on the box-and-whisker plot, find: Minimum, Maximum, Q 1, Q 2, Q 3, and IQR .

With the box-and-whisker plot open in StatCrunch, place your cursor on the solid part of the box. A small window will pop up, as shown in Figure 32.

Figure 32. Pop-up window for box-and-whisker plot.

• Type each of these 6 measures in the word processing file ComputerLab1B just below the box-and-whisker plot that you just pasted.

Activity 12. Apply tools of descriptive statistics to subsets of data.

If a data file includes both qualitative and quantitative variables, tools of descriptive statistics can be applied to subsets of the data.

For example, the Stat 101 survey questionnaire in Activity 3 in Computer Lab 1 contained two variables—Gender (qualitative) and Grade (quantitative). You will recall that twenty students responded to this survey; in analyzing the survey responses, typically summary measures would be computed, or graphs would be created, for all twenty students.

Another alternative is to break the data into two subsets: a grades subset for male students and a grades subset for female students. Summary measures could then be computed, or graphs created, for each subset, and results of the two subsets could be compared.

Task 27. Work with and Compare Subsets

The task at hand, then, is to:

• Open the STAT101 Survey Responses data file from your My Data folder at StatCrunch.com.
• Compute the mean, median, standard deviation, and 50th and 90th percentiles ( P 50, P 90) for the grades for both the male and female subsets.
• Create box-and-whisker plots for the grades of both the male and female subsets.

Figure 33 shows the StatCrunch output for the measures, mean, median, standard deviation, and 50th and 90th percentiles ( P 50, P 90), in table form.

Figure 33. Mean, Median, Standard Deviation, P50, P90 for Grades

Figure 34 shows the Stat 101 survey.

Figure 34. Stat101 survey.

In Activity 3 in Computer Lab 1, you created the StatCrunch data file Stat101 Survey Responses consisting of the twenty student responses for the two variables Gender and Grade. You then saved this data file to your My Data folder on the StatCrunch website.

Open this data file, following the guided solutions steps below.

Guided Solution 27a

Open the Stat101 Survey Responses file from the My Data folder on the StatCrunch website.

• Sign in to StatCrunch. (If you need help, see Accessing and Working in StatCrunch on the course home page.)
• Click MyStatCrunch.

Click My Data (see Figure 35.)

Figure 35. My Data Link in MyStatCrunch

Click the STAT101 Survey Responses link to open the STAT101 data table. (See Figure 36)

Figure 36. STAT101 Survey Responses link in your My Data folder on StatCrunch.

Guided Solution 27b

Computing the Mean, Median, Standard Deviation, P 50, and P 90 for Student Grades For Male and Female Subsets.

Here, with the STAT101 Survey Responses data file open, you will create the Mean, Median, Standard Deviation, P 50, P 90 table for Grades shown in Figure 33.

• In the Select columns box, click the variable Grade.
• In the Group by box, select the variable Gender.
• In the Statistics box, hold the Crtl key down while clicking on Mean, Median, and Standard Deviation.

In the Percentiles box, type 50, 90. See Figure 37.

Figure 37. Summary Statistics Window: Mean, Median, Standard Deviation, P 50, and P 90 for Grades: Male and Female Subsets

• Click Compute to display the Mean, Median, Standard Deviation, and P 50 and P 90 table as shown in Figure 33.

Guided Solution 27c

Copy the Mean, Median, Standard Deviation, P 50, P 90 table into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Mean, Median, Standard Deviation, P 50, P 90 for Grades for Male and Female Subsets of the Stat101 Students below the bottom item.

Task 28. Interpretation - Mean, Median, Standard Deviation, P 50, P 90 Table

Insert the questions below into your ComputerLab1B word processing file, under the Mean, Median, Standard Deviation, P 50, P 90 table you just pasted.

Based on your review of the pasted Mean, Median, Standard Deviation, P 50, P 90 table, type your answers to these questions in the solutions spaces provided. (If you need help answering these questions, see the Solutions section that follows them.)

The mean grade for the female students = _____ and the mean grade for the male students = _____.

Which subgroup of students displayed the greatest variability of grades? Explain.

Interpret the P 50 and P 90 grades for each group of students.

Is the subset of grades for the female students positively or negatively skewed? Interpret this result.

Is the subset of grades for the male students positively or negatively skewed? Interpret this result.

Solutions to Task 28

• The mean grade for the female students = 88.75 and the mean grade for the male students = 60.4167.
• The standard deviation for females = 6.4086, and the standard deviation for males = 17.5108. This means that the grades for the males were much more variable. The typical female grade was only approximately 6.4086 marks above or below the mean of 88.75 marks, while the typical male grade was approximately 17.5108 marks above or below the mean of 60.4167 marks.

For the female students, the P 50 = 90 and the P 90 = 95. This means that 50% of the female students got 90% or less, while 90% of the female students got 95% or less.

For the male students, the P 50 = 55 and the P 90 = 90. This means that 50% of the male students got 55% or less, while 90% of the male students got 90% or less.

• The female grades are negatively skewed, as the mean of 88.75 is less than the median of 90. This means that, while most of the students got above-average grades, there were a few non-typical low grades.
• The male grades are positively skewed, as the mean of 60.4167 is greater than the median of 55. This means that, while most of the male students got below-average grades, there were a few non-typical high grades.

In the next section, you will create separate box-and-whisker plots for the male and female student subsets.

Task 29. Create a box-and-whisker plot.

Here, with the StatCrunch data file STAT101 Survey Responses open, you will create box-and-whisker plots for both the female and male subsets of student grades. Figure 38 shows the box-and-whisker plots.

Figure 38. Box-and-whisker plots for female and male subsets of student grades.

Guided Solution 29a

Create box-and-whisker plots for both the male and female subsets of student grades.

• With the StatCrunch data file STAT101 Survey Responses open, click the menu option sequence Graph → Boxplot.
• In the Select Columns box, click the variable Grade.
• In the Group by box, select Gender.
• In the Graph properties section, in the box X -axis label, type Student Grades and select vertical lines.
• In the For multiple graphs section, select both Use same X -axis and Use same Y -axis. See Figure 39.

Figure 39. Boxplot window.

• Click Compute to display the box-and-whisker plot shown in Figure 38 above.

Guided Solution 29b

Copy the box-and-whisker plots into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Box-and-whisker Plots for the Grades for both the Male and Female Subsets below the bottom item.

Task 30. Interpretation of Plots

With the box-and-whisker plots displayed in the Boxplot window in StatCrunch, quickly determine the six measures for Grades for each subset: Minimum, Maximum, Q 1, Q 2, Q 3, and IQR . Note the guided solution below.

Guided Solution 30

Based on the box-and-whisker plots for each subset in the StatCrunch boxplot, find: Minimum, Maximum, Q 1, Q 2, Q 3, and IQR for each subset.

With the two box-and-whisker plots displayed in the Boxplot window of StatCrunch, place your cursor in the Male Subset box; a small window will pop up as shown in Figure 40.

Figure 40. Pop-up window for the box-and-whisker plot for the males subset.

With the two Box-and-whisker Plots displayed in the Boxplot window of StatCrunch, move the cursor to touch the solid part of the Female Subset box and a small window will pop up as shown in Figure 41.

Figure 41. Pop-up window for the box-and-whisker plot for the females subset.

• Open your word processing file ComputerLab1B. In it, type each set of six measures below the box-and-whisker plot that you just pasted.

Activity 13. Conduct contingency table analysis: Relationship between two survey variables.

A contingency table is a popular statistical tool used to analyze the relationship between two qualitative survey variables. NOTE: Although this table is not covered in Chapter 2 of your eText, you are responsible for creating and interpreting this type of statistical table in StatCrunch in the Computer Component of this course.

Figure 42 shows a survey questionnaire that was completed by 25 customers who shop regularly at SuperMart, a neighbourhood supermarket. The survey responses have been entered in a StatCrunch data file called SuperMart. This data file is available from the AU Math216 2020 StatCrunch Group folder at statcrunch.com.

Figure 42. SuperMart Survey

Task 31. Create a contingency table.

Here, you will create a contingency table for the survey responses in the SuperMart data file, with Gender displayed as the row variable, and Discount displayed as the column variable. Display the Row Percents. The completed Contingency Table is shown in Figure 43.

Figure 43. Contingency Table: Gender vs . Discount

According to the contingency table in Figure 43:

• The number of females who responded No to using discount coupons is 1.
• The number of females who responded Yes to using discount coupons is 16.
• The number of males who responded No to using discount coupons is 7.
• The number of males who responded Yes to using discount coupons is 1.

Guided Solution 31a

Open the SuperMart data file from the Groups folder in StatCrunch.

• Go to the StatCrunch MATH 216 Groups page and sign in. (If you need help, see Open a Groups data file in Accessing and Working in StatCrunch on the course home page.)
• Find and click the SuperMart link to open this StatCrunch data file. You should now see the SuperMart data file, showing two variables, Gender and Discount, and 25 rows of survey responses.

Guided Solution 31b

Create a contingency table, Gender vs . Discount.

• With the SuperMart data file open, Click the menu option sequence Stat → Tables → Contingency → With Data.
• In the Row variable box, select Gender.
• In the Column variable box, select Discount.
• In the Display box, select Row Percent.
• Click Compute to create the contingency table shown in Figure 43 above.

Guided Solution 31c

Copy the contingency table into your word processing file ComputerLab1B.

• Open the word processing file ComputerLab1B, and type Contingency Table: Gender vs . Discount below the bottom item.

Task 32. Interpretation - Interpret the contingency table results in terms of the two variables Gender and Discount.

Insert the questions below into your ComputerLab1B word processing file, under the contingency table you just pasted.

Based on your review of the pasted contingency table, type your answers to these questions in the solutions spaces provided. (If you need help answering these questions, see the Solutions section that follows them.)

Compare the percent of females typically using the discount coupons with the percent of males typically using discount coupons. (These are called “row percents”.)

Based on the row percents identified in #1 above, what can you state regarding the relationship between Gender and Discount? Explain.

Solutions to Task 32

• While 94.12% of the female customers typically use the discount coupons, only 12.5% of the male customers typically do so.
• In general, female customers typically use the discount coupons, while male customers typically do not use the discount coupons.