Mathematics 216 Computer-oriented Approach to Statistics

Study Guide :: Unit 1

Descriptive Statistics

Introduction

For most of us, the word statistics triggers a mental image of lots and lots of numbers. In a sense, that image is not far removed from the subject you are about to study.

The first thing you will do as a statistics practitioner is collect a body of numerical facts that we call raw data. The field of statistics is particularly relevant in today's information-based economy, in which an enormous amount of raw data is immediately available through electronic databases, the Internet, and computerized point-of-sale terminals in businesses and organizations.

But numbers are only the beginning—it is what one does with them that brings meaning to them. After collecting raw data, you must organize it and present it in a way that allows coherent, relevant information about a problem or decision to emerge. The set of methods used to collect, summarize, organize, and present data is known as descriptive statistics, the subject of Unit 1.

You will begin the unit by familiarizing yourself with key terms. Next, you will learn how to organize and present data. While it is a common practice to present data in a table, as a frequency distribution, graphical representations such as line graphs, histograms, bar charts, pie charts, stem-and-leaf plots, and dot plots make it easier for the viewer to comprehend the data.

In your presentation of data, you must include relevant summary measures, which summarize and describe the characteristics and properties of the particular data set. It is customary to provide three types of measures:

  • measures of central tendency, such as the mean, median, and mode;
  • measures of variability, such as the standard deviation, variance, and coefficient of variation;
  • and measures of position, such as quartiles, percentiles, and z-scores.

As you progress through Unit 1, you will see how descriptive statistics can provide valuable input for making key decisions or solving pressing problems. As seemingly unrelated raw data takes on meaningful form, you will appreciate how these numbers can provide information about our lives, our society, and our universe.

Note: In this course, each set of navigation instructions is provided the first time it is needed, and summarized navigation sheets are posted on the course home page.

Overview of Statistics

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • descriptive statistics; inferential statistics
    • parameter
    • population
    • sample
    • statistic; statistics
  2. Distinguish between population and sample.
  3. Distinguish between parameter and statistic.
  4. Distinguish between descriptive statistics and inferential statistics.
Required Reading

Elementary Statistics, Part 1, Chapter 1, Section 1.1, An Overview of Statistics

Important Note: For help accessing the eText reading, see Navigating Your eText on the course home page.

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

For help accessing the solutions to the Try It Yourself Examples, see Navigating Your eText on the course home page.

Exercises in Your eText

Do the following exercises in your eText:

Part 1, Chapter 1, Section 1.1 Exercises 5, 9, 11, 13, 19, 35, 37, 47 (pages 6-8). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

To view the solutions to the odd-numbered exercises, see Navigating Your eText on the course home page.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 1 Section 1.1 are available on the textbook publisher’s MyLab website. To take advantage of these resources:

  1. Go to www.pearsonmylab.com and sign in. (You may wish to use the Chrome browser for access to Pearson web pages.) Please bookmark this page, as you will return to it often during this course.
  2. Open the Math216 7e V3 link near the top left of your screen.
  3. Click the menu option Multimedia Library.
  4. Select the appropriate chapter and section; in this case, Chapter 1, Section 1.1.
  5. Select the desired media type (e.g., Section Video Lectures).
  6. Click the Find Now button.
  7. Click on the link(s) that appear to view the multimedia item(s) you selected.

Data Classification

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • nominal, ordinal, interval, and ratio levels of measurement
    • qualitative data; quantitative data
  2. Distinguish between the types of data: qualitative data and quantitative data.
  3. Distinguish among the different levels of measurement: nominal, ordinal, interval, and ratio levels of measurement.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 1, Section 1.2, Data Classification

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Chapter 1, Section 1.2 Exercises 9, 15, 21, 25 (pages 13-15). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 1 Section 1.2 are available on the textbook publisher’s MyLab website.

Data Collection and Experimental Design

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • census
    • confounding variable
    • double blind experiment; experiment
    • matched pair
    • observational study
    • randomization
    • sampling error
    • simple random sample
    • simulation
    • survey
  2. Identify and explain the four methods of collecting data.
  3. Explain the simple random sampling technique.
  4. Use a random number table or StatCrunch to generate simple random samples based on given sampling situations.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 1, Section 1.3, Data Collection and Experimental Design (pages 17‑21)

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Chapter 1, Section 1.3 Exercises 11, 13, 23 (pages 24-25). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 1 Section 1.3 are available on the textbook publisher’s MyLab website.

Chapter 1 Review (Extra Online Practice)

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to the computer lab section of this unit.

Review Learning Objectives

Before proceeding to the online exercises, briefly review the Learning Objectives for each of the following topics, from previous sections of this Study Guide:

  • Overview of Statistics
  • Data Classification
  • Data Collection
Optional Practice in the MyLab Study Plan

For more practice on the topics/sections of Chapter 1, visit Pearson MyLab, and work interactively through the exercises in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page. To go to these optional exercises:

  1. Go to www.pearsonmylab.com and sign in. Please bookmark this page, as you will return to it often during this course.
  2. Click on Math216 7e V3 on the left of your screen.
  3. Click the menu option Study Plan.
  4. Click All Chapters at the top of your screen.
  5. Click on the chapter you would like to review.
  6. Click on the chapter section you would like to review.
  7. Click on an exercise and start your practice session.

Computer Lab 1A

In Computer Lab 1, you will begin to learn to use a statistical software called StatCrunch to develop solutions to exercises related to topics in the eText’s Chapter 1.

Computer Lab 1A Detailed Instructions

For your Computer Lab 1A activities, and step-by-step instructions (Guided Solutions) to familiarize you with StatCrunch, see Computer Lab 1A.

Computer Lab 1A Quick Reviews

The Computer Lab Quick Reviews (QRs) summarize a few key steps (but not all steps) needed to complete each Activity in the Computer Labs. These QRs will be useful when you are preparing for the computer components of the assignments, midterm exam, and final exam. To access the QRs, click MATH 216 Computer Lab 1A QRs on your course home page.

Frequency Distributions and Their Graphs

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • class boundaries; class limits; class midpoints
    • cumulative frequency; relative frequency
    • frequency distribution
    • frequency histogram; relative frequency histogram
    • frequency polygon
    • ogive
  2. Construct a frequency distribution in a table format that would include:
    classes, class midpoints, frequencies, relative frequencies, cumulative frequencies, boundaries.
  3. Construct the following graphs:
    frequency histogram, frequency polygon, relative frequency histogram, ogive.
  4. Given a frequency distribution, or related graph, interpret the following results in the context of the problem:
    frequencies, relative frequencies, cumulative frequencies.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 2, Section 2.1, Descriptive Statistics (pages 38-48)

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Chapter 2, Section 2.1 Exercises 29, 31, 39, 43 (pages 51-54). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 2 Section 2.1 are available on the textbook publisher’s MyLab website.

More Graphs and Displays

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • paired data sets
    • Pareto chart; pie chart; time series chart
    • scatter plot; stem-and-leaf plot
  2. Construct a stem-and-leaf plot, and then interpret the plot results in the context of the problem.
  3. Use StatCrunch to construct a pie chart and interpret the chart results in the context of the problem.
    Note: You are not required to construct a pie chart by hand.
  4. Construct a Pareto chart, and interpret the chart results in the context of the problem.
  5. Graph a paired data set, and interpret the graph results in the context of the problem.
  6. Construct a time series chart, and interpret the chart results in the context of the problem.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 2, Section 2.2, More Graphs and Displays (pages 55-61). Omit the section on dot plots.

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Section 2.2 Exercises 13, 15, 17, 27, 29, 31 (pages 63-65). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 2 Section 2.2 are available on the textbook publisher’s MyLab website.

Measures of Central Tendency

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • bimodal
    • grouped data
    • mean; median; mode
    • measure of central tendency
    • outlier
    • skewed left distribution; skewed right distribution; symmetric distribution; uniform distribution
    • weighted mean
  2. Compute the mean, median, and mode for raw (ungrouped) data.
  3. Compute the weighted mean.
  4. Compute the mean of a frequency distribution (grouped data).
  5. Explain how the shape of a distribution affects the relation between the mean, median, and mode.
  6. Identify which measure of central tendency is most appropriate to use for different data sets.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 2, Section 2.3, Measures of Central Tendency (pages 67-73)

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Chapter 2, Section 2.3 Exercises 17, 21, 23, 31, 35, 37, 39, 41, 43, 49 (pages 75-78). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 2 Section 2.3 are available on the textbook publisher’s MyLab website.

Measures of Variation

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • deviation; coefficient of variation
    • population standard deviation; sample standard deviation
    • population variance; sample variance
    • range
  2. Compute the range, variance, and standard deviation for raw (ungrouped) population or sample data. Interpret your results in terms of the context of the problem.
  3. Use the Empirical Rule to estimate the percent of the sample or population data that falls between two given values.
  4. Use Chebychev's Theorem to estimate the percent of the sample or population data that falls between two given values.
  5. Compute the mean and standard deviation for grouped data.
  6. Use the coefficient of variation to compare variability of multiple data sets.
Required Reading

Elementary Statistics, Chapter 2, Section 2.4, Measures of Variation (pages 82-92)

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Chapter 2, Section 2.4 Exercises 13, 15, 19, 29, 31, 35, 39, 45 (pages 93-98). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 2 Section 2.4 are available on the textbook publisher’s MyLab website.

Measures of Position

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Explain the meaning of the key terms:
    • quartiles
    • interquartile range (IQR)
    • box-and-whisker plot
    • percentiles
    • z-scores
  2. Compute quartiles for raw (ungrouped) data.
  3. Sketch a box-and-whisker plot, given the maximum, minimum, and the quartiles.
  4. Compute z-scores.
  5. Interpret quartiles, percentiles, box-and-whisker plots, z-scores.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 2, Section 2.5, Measures of Position (pages 102-108)

Try It Yourself Examples

Work through each Try It Yourself Example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Chapter 2, Section 2.5 Exercises 11, 13, 23, 31, 33, 35, 37, 47 (pages 109-112). Write out the step-by step-solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 2 Section 2.5 are available on the textbook publisher’s MyLab website.

Chapter 2 Review (Extra Online Practice)

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to the computer lab section of this unit.

Review Learning Objectives

Before proceeding to the online exercises, briefly review the Learning Objectives for each of the following topics, from previous sections of this Study Guide:

  • Frequency Distributions and Their Graphs
  • More Graphs and Displays
  • Measures of Central Tendency
  • Measures of Variation
  • Measures of Position
Optional Practice in the MyLab Study Plan

If you would like more practice on the various topics/sections of Chapter 2, you may wish to visit Pearson MyLab, the website that accompanies your textbook, and work interactively through online exercises offered in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Computer Lab 1B

In Computer Lab 1B, you will learn to use the statistical software called StatCrunch to develop solutions to exercises related to topics in the eText’s Chapter 2.

Computer Lab 1B Detailed Instructions

For your Computer Lab 1B activities, and step-by-step instructions (Guided Solutions) to familiarize you with StatCrunch, see Computer Lab 1B.

Computer Lab 1B Quick Reviews

The Quick Review (QRs) summarize a few key steps (but not all steps) needed to complete each Activity in Computer Lab 1B. These QRs will be useful when you are preparing for the computer components of the assignments, midterm exam, and final exam. To access the QRs, click Computer Lab 1B QRs.

Self-Test 1

To access Self-Test 1, click MATH 216 Self-Test 1.

It is important that you work through all the exercises in the unit self-tests and the eText chapter quizzes. They are designed to, along with the unit assignments, help you master the content presented in each unit.

Each unit self-test has two parts: one on theory (A) and one on computer work (B). Working through these will help you review key exercises in the unit, which will help you prepare for assignments and exams.

Assignment 1

After completing Self-Test 1, complete Assignment 1, which you will find on the course home page. Submit your solutions to this assignment for marking using the drop box on the course home page.