Discover relationships with this data visualization teaching tool.

Statistics instructors, have you explored Gapminder yet? It’s one of our favorite data visualization resources! It’s a free site offering many videos and tools, including a graphical simulator depicting 5 dimensions of real-world data in 2D.

Check out how you can use this tool in your classroom to show students the changing relationships between demographic, economic, and societal variables animated over time.

Change the variables to include life expectancy, average income, population, unemployment rate, CO2 emissions, amount of cell phone users, and more. Pinpoint specific historical events to discover their impact through data visualization.

 

  • Correlating development data
    Select Chart and compare different indicators, such as Life Expectancy and Income. What correlations can be found?
  • Analyzing trends
    Try choosing Life Expectancy and analyzing changes over time (select Time for the x axis.) Track selected countries by selecting them, clicking the Trails box, and playing the animation.
  • Mapping development indicators
    Select Map and look for patterns by selecting different development indicators for the countries.

Discovering Statistics and Data cover

 

Along with many downloadable data sets and computational technology instructions, this data visualization tool is available on our free web resource, stat.hawkeslearning.com.

This tool is also integrated within our new text, Discovering Statistics and Data, to bring students toward a deeper understanding of statistics and how we can tell stories through data analysis.

Let us know if you want an exam copy at 1-800-426-9538 or sales@hawkeslearning.com!

 

 


FREE TO USE! CC-BY GAPMINDER.ORG.

SHOWING A FREE VISUALIZATION FROM GAPMINDER.ORG, CC-BY LICENSE.

 

Integrate Developmental Math with Statistics in Corequisite Course

Cover of Discovering Statistics and Data Plus Integrated ReviewDiscovering Statistics and Data Plus Integrated Review leads students through the study of statistics with an introduction to data.

It pays homage to the technology-driven data explosion by helping students understand the context behind future statistical concepts to be learned. Students are introduced to what data is, how we measure it, where it comes from, how to visualize it, and what kinds of career opportunities involve its analysis and processing.

 

This integrated course enhances curriculum-level statistics with applicable review skills to shorten the prerequisite sequence without compromising competency. Target specific remediation needs for just-in-time supplementation of foundational concepts.

Table of Contents:

Chapter 1: Statistics and Problem Solving

1.1-1.8: Introduction to Statistical Thinking

Chapter 2: Data, Reality, and Problem Solving

2.R.1: Problem Solving with Whole Numbers
2.R.2: Introduction to Decimal Numbers
2.1: The Lords of Data
2.2: Data Classification
2.3: Time Series Data vs. Cross-Sectional Data
Chapter 2 Review

Chapter 3: Visualizing Data

3.R.1: Introduction to Fractions and Mixed Numbers
3.R.2: Decimals and Fractions
3.R.3: Decimals and Percents
3.R.4: Reading Graphs
3.R.5: Constructing Graphs from a Database
3.R.6: The Real Number Line and Inequalities
3.1: Frequency Distributions
3.2: Displaying Qualitative Data Graphically
3.3: Constructing Frequency Distributions for Quantitative Data
3.4: Histograms and Other Graphical Displays of Quantitative Data
3.5: Analyzing Graphs
Chapter 3 Review

Chapter 4: Describing and Summarizing Data From One Variable

4.R.1: Addition with Real Numbers
4.R.2: Subtraction with Real Numbers
4.R.3: Multiplication and Division with Real Numbers
4.R.4: Exponents and Order of Operations
4.R.5: Evaluating Algebraic Expressions
4.R.6: Evaluating Radicals
4.1: Measures of Location
4.2: Measures of Dispersion
4.3: Measures of Relative Position, Box Plots, and Outliers
4.4: Data Subsetting
4.5: Analyzing Grouped Data
4.6: Proportions and Percentages
Chapter 4 Review

Chapter 5: Discovering Relationships

5.R.1: The Cartesian Coordinate System
5.R.2: Graphing Linear Equations in Two Variables: Ax + By = C
5.R.3: The Slope-Intercept Form: y = mx + b
5.1: Scatterplots and Correlation
5.2: Fitting a Linear Model
5.3: Evaluating the Fit of a Linear Model
5.4: Fitting a Linear Time Trend
5.5: Scatterplots for More Than Two Variables
Chapter 5 Review

Chapter 6: Probability, Randomness, and Uncertainty

6.R.1: Multiplication and Division with Fractions and Mixed Numbers
6.R.2: Least Common Multiple (LCM)
6.R.3: Addition and Subtraction with Fractions
6.R.4: Fractions and Percents
6.1: Introduction to Probability
6.2: Addition Rules for Probability
6.3: Multiplication Rules for Probability
6.4: Combinations and Permutations
6.5: Bayes’ Theorem
Chapter 6 Review

Chapter 7: Discrete Probability Distributions

7.R.1: Order of Operations with Real Numbers
7.R.2: Solving Linear Inequalities
7.1: Types of Random Variables
7.2: Discrete Random Variables
7.3: The Discrete Uniform Distribution
7.4: The Binomial Distribution
7.5: The Poisson Distribution
7.6: The Hypergeometric Distribution
Chapter 7 Review

Chapter 8: Continuous Probability Distributions

8.R.1: Area
8.R.2: Solving Linear Equations: ax + b = c
8.R.3: Working with Formulas
8.1: The Uniform Distribution
8.2: The Normal Distribution
8.3: The Standard Normal Distribution
8.4: Applications of the Normal Distribution
8.5: Assessing Normality
8.6: Approximation to the Binomial Distribution
Chapter 8 Review

Chapter 9: Samples and Sampling Distributions

9.R.1: Ratios and Proportions
9.1: Random Samples
9.2: Introduction to Sampling Distributions
9.3: The Distribution of the Sample Mean and the Central Limit Theorem
9.4: The Distribution of the Sample Proportion
9.5: Other Forms of Sampling
Chapter 9 Review

Chapter 10: Estimation: Single Samples

10.1: Point Estimation of the Population Mean
10.2: Interval Estimation of the Population Mean
10.3: Estimating the Population Proportion
10.4: Estimating the Population Standard Deviation or Variance
Chapter 10 Review

Chapter 11: Hypothesis Testing: Single Samples

11.R.1: Translating English Phrases and Algebraic Expressions
11.R.2: Order of Operations with Fractions and Mixed Numbers
11.1: Introduction to Hypothesis Testing
11.2a: Testing a Hypothesis about a Population Mean with Sigma Known
11.2b: Testing a Hypothesis about a Population Mean with Sigma Unknown
11.2c: Testing a Hypothesis about a Population Mean using P-values
11.3: The Relationship between Confidence Interval Estimation and Hypothesis Testing
11.4a: Testing a Hypothesis about a Population Proportion
11.4b: Testing a Hypothesis about a Population Proportion using P-values
11.5: Testing a Hypothesis about a Population Standard Deviation or Variance
11.6: Practical Significance vs. Statistical Significance
Chapter 11 Review

Chapter 12: Inferences about Two Samples

12.1a: Inference about Two Means: Independent Samples with Sigma Known
12.1b: Inference about Two Means: Independent Samples with Sigma Unknown
12.2: Inference about Two Means: Dependent Samples (Paired Difference)
12.3: Inference about Two Population Proportions
Chapter 12 Review

Chapter 13: Regression, Inference, and Model Building

13.1: Assumptions of the Simple Linear Model
13.2: Inference Concerning β1
13.3: Inference Concerning the Model’s Prediction
Chapter 13 Review

Chapter 14: Multiple Regression

14.1: The Multiple Regression Model
14.2: The Coefficient of Determination and Adjusted R2
14.3: Interpreting the Coefficients of the Multiple Regression Model
14.4: Inference Concerning the Multiple Regression Model and its Coefficients
14.5: Inference Concerning the Model’s Prediction
14.6: Multiple Regression Models with Qualitative Independent Variables
Chapter 14 Review

Chapter 15: Analysis of Variance (ANOVA)

15.1: One-Way ANOVA
15.2: Two-Way ANOVA: The Randomized Block Design
15.3: Two-Way ANOVA: The Factorial Design
Chapter 15 Review

Chapter 16: Looking for Relationships in Qualitative Data

16.1: The Chi-Square Distribution
16.2: The Chi-Square Test for Goodness of Fit
16.2: The Chi-Square Test for Association
Chapter 16 Review

Chapter 17: Nonparametric Tests

17.1: The Sign Test
17.2: The Wilcoxon Signed-Rank Test
17.3: The Wilcoxon Rank-Sum Test
17.4: The Rank Correlation Test
17.5: The Runs Test for Randomness
17.6: The Kruskal-Wallis Test
Chapter 17 Review


Interested in exploring this course?

 

Contact us today at sales@hawkeslearning.com or 1-800-426-9538.

Introducing the Third Edition of Discovering Statistics and Data

Discovering Statistics and Data coverWe’re proud to announce the new edition of Discovering Statistics and Data!

This new edition pays homage to modern day’s technology-driven data explosion, helping students understand the context behind future statistical concepts to be learned and explaining why the study of statistics is critical.
View a free sample of the new edition of Discovering Statistics and Data.

The text opens by describing the necessity of understanding the data around us, introducing students to what data is, how we measure it, where it comes from, how to visualize it, and what kinds of career opportunities surround its analysis and processing. This focus makes upcoming content more meaningful for students and then challenges them to think with statistics. Request an examination copy.


NEW features include:

  • Greater focus on data – Introductory chapters place a strong emphasis on helping students understand where data comes from, data visualization techniques, “Big Data,” and the problems arising from having large data sets.
  • Downloadable data sets – More real data sets are available for download, including over 15 large data sets and one giant data set. 
  • More technology integration – Detailed instruction using graphing calculators, Excel, Minitab, and R Statistical language are included.
  • Real-world applications – Larger scale chapter projects challenge students and brief, relatable articles engage readers.
  • Expanded exercises and examples – Over 60 examples and 200 exercises, including new conceptual questions, have been added.
  • Pedagogy modernization – GAISE guidelines were carefully considered and incorporated, and the most current P-value significance testing recommendations published by the ASA for guidance on hypothesis testing are included.
  • Virtual simulations and games – Students develop conceptual understanding and statistical literacy through hands-on interactives and simulations.

Table of Contents:

1. Statistics and Problem Solving

The Meaning of Data
Statistics as a Career
The Data Explosion
Modern Computing, Networks, and Statistics
Big Data
Introduction to Statistical Thinking
Descriptive vs. Inferential Statistics
The Consequences of Statistical Illiteracy

2. Data, Reality, and Problem Solving

Collecting Data
Data Classification
Time Series Data vs. Cross-Sectional Data
Data Resources

3. Visualizing Data

Frequency Distributions
Displaying Qualitative Data Graphically
Constructing Frequency Distributions for Quantitative Data
Histograms and Other Graphical Displays of
Quantitative Data
Analyzing Graphs

4. Describing and Summarizing Data from One Variable

Measures of Location
Measures of Dispersion
Measures of Relative Position, Box Plots, and Outliers
Data Subsetting
Analyzing Grouped Data
Proportions and Percentages

5. Discovering Relationships

Scatterplots and Correlation
Fitting a Linear Model
Evaluating the Fit of a Linear Model
Fitting a Linear Time Trend
Scatterplots for More Than Two Variables

6. Probability, Randomness, and Uncertainty

Introduction to Probability
Addition Rules for Probability
Multiplication Rules for Probability
Combinations and Permutations
Combining Probability and Counting Techniques
Bayes’ Theorem

7. Discrete Probability Distributions

Types of Random Variables
Discrete Random Variables
The Discrete Uniform Distribution
The Binomial Distribution
The Poisson Distribution
The Hypergeometric Distribution

8. Continuous Probability Distributions

The Uniform Distribution
The Normal Distribution
The Standard Normal Distribution
Applications of the Normal Distribution
Assessing Normality
Approximations to Other Distributions

9. Samples and Sampling Distributions

Random Samples and Sampling Distributions
The Distribution of the Sample Mean and the Central Limit Theorem
The Distribution of the Sample Proportion
Other Forms of Sampling

10. Estimation: Single Samples

Point Estimation of the Population Mean
Interval Estimation of the Population Mean
Estimating the Population Proportion
Estimating the Population Standard Deviation or Variance
Confidence Intervals Based on Resampling (Bootstrapping) (Courseware only)

11. Hypothesis Testing: Single Samples

Introduction to Hypothesis Testing
Testing a Hypothesis about a Population Mean
The Relationship between Confidence Interval
Estimation and Hypothesis Testing
Testing a Hypothesis about a Population Proportion
Testing a Hypothesis about a Population Standard Deviation or Variance
Practical Significance vs. Statistical Significance

12. Inferences about Two Samples

Inference about Two Means: Independent Samples
Inference about Two Means: Dependent Samples (Paired Difference)
Inference about Two Population Proportions
Inference about Two Population Standard Deviations or Variances

13. Regression, Inference, and Model Building

Assumptions of the Simple Linear Model
Inference Concerning β1
Inference Concerning the Model’s Prediction

14. Multiple Regression

The Multiple Regression Model
The Coefficient of Determination and Adjusted R2
Interpreting the Coefficients of the Multiple Regression Model
Inference Concerning the Multiple Regression Model and its Coefficients
Inference Concerning the Model’s Prediction
Multiple Regression Models with Qualitative Independent Variables

15. Analysis of Variance (ANOVA)

One-Way ANOVA
Two-Way ANOVA: The Randomized Block Design
Two-Way ANOVA: The Factorial Design

16. Looking for Relationships in Qualitative Data

The Chi-Square Distribution
The Chi-Square Test for Goodness of Fit
The Chi-Square Test for Association

17. Nonparametric Tests

The Sign Test
The Wilcoxon Signed-Rank Test
The Wilcoxon Rank-Sum Test
The Rank Correlation Test
The Runs Test for Randomness
The Kruskal-Wallis Test

18. Statistical Process Control (Courseware only)


Request an examination copy.

Want to know more? Contact us at sales@hawkeslearning.com!

Interactive and Relevant Applications of Statistics

Hawkes statistics courses include games and simulations that help students apply key concepts to the world outside of the classroom. Check these out below! If you’re an instructor who would like to explore these games and simulations yourself, sign up for free student access today.

1. Games of Chance

gamesofchance2

Relevant Application:
This lesson helps students apply the concept of the expected value of a random variable to winning or losing games. Students develop a rational approach to analyzing decisions that involve risk. After all, many business decisions—such as purchasing new equipment, hiring additional employees, and expanding into new markets—involve some kind of risk, and students need to assess these situations as best as they can.

Learn Key Concepts:

  • Basic probability distribution
  • Binomial distribution function
  • Hypergeometric distribution function

2. Direct Mail

directmail2

Relevant Application:
Even in today’s digital world, direct mail marketing remains one of the most viable and proven strategies to connect with customers.

Active Learning Approach:
By assuming the role of a direct mail marketing manager, students start off with $20,000. They are then tasked with developing a strategy by finding mailing lists that will produce sufficient sales, using confidence intervals to determine which lists to use to reach their $40,000 goal.

They win when they correctly formulate which questions they need to solve, collect the data, and analyze the data to evaluate potential risk and profitability for each mailing list.

Learn Key Concepts:
The game provides an environment in which students apply statistical concepts while making business decisions. They also learn the following:

  • Confidence intervals
  • Experimentation
  • Statistical analysis
  • Inference

3. Estimating Population Proportions

estimatingpopulationproportions

Relevant Application:
Students might not realize at first how many decisions involve measurements of a population attribute. For example, television stations base advertising charges on
ratings that reflect the percentage of viewers who watch a particular show. Political analysts are concerned with the fraction of voters who prefer a certain candidate. No
matter the field, estimating population proportions gives us greater insight into the data given to us.

Active Learning Approach:
In the game, students see a box filled with red and blue balls, and are asked to estimate the proportion of red balls in the population. They can draw sample sizes of 20, 50, or
100 to help them estimate the population proportion.

Learn Key Concepts:

  • Determine the minimum sample size for a particular confidence level.
  • Construct a confidence interval for a population proportion.

4. Central Limit Theorem with Proportions

Relevant Application:
In many decisions, the variable of interest is a proportion. A university may want to know the fraction of first-year students with low grades in order to provide more support and resources for them. Manufacturers may be concerned with the fraction of parts that are defective.

Active Learning Approach:
Students see a box of red and blue balls, then draw three samples to calculate the sample proportions for each sample taken. Students draw samples again after being informed that samples of first 20 balls and then 40 balls were drawn 200 times to determine the proportion of the number of red balls to the total number of balls chosen. Students then view the data, including tables and histograms, to understand that the sampling distribution of the sampling proportion is approximately normal.

Learn Key Concepts:
Determine p-hat using the Central Limit Theorem for population proportions.

SIMULATIONS

1. Name That Distribution

namethatdistribution

Relevant Application:
This concept builder strengthens analytical skills in distribution recognition and data analysis. By detecting symmetric or skewed data, students will begin to understand how to apply this knowledge in the real world.

Active Learning Approach:
Students are asked to identify the type of distribution from a given histogram, frequency/relative frequency distribution, statistics table, or set of sample data. They
can increase the number of intervals on the histogram or frequency distribution, view different sample displays, or choose to view a hint before submitting their answer.

Learn Key Concepts:

  • Analyze the histogram, frequency, statistics, and sample data of a distribution.
  • Identify different distribution types: uniform, normal, exponential, chi-square, Poisson, and mystery.

2. Central Limit Theorem

The simulation can run automatically and in bursts. This image shows histograms for n=5, n=15, and n=30. It includes the histogram of the parent function.

Relevant Application:
This simulation shows students how to use samples to make useful predictions about a population. Since many population sizes are too large to have their data collected and analyzed, we turn to the Central Limit Theorem for help.

The visual nature of this simulation lets students truly comprehend how the sample means from any population are normally distributed, regardless of the original
population’s distribution.

Active Learning Approach:
Students select a parent distribution and set the sample sizes and the burst rate. They choose the desired distribution type: exponential, chi-square, normal, Poisson, or bi-modal. Students can decide to run the simulation a set number of times or automatically, which will keep the simulation running.

Learn Key Concepts:

  • Sample population
  • Mean
  • Variance
  • Standard deviation
  • Distribution type

3. Type II Error

You can select the plus or minus buttons for alpha, true mean, and sample size to change the graph. The shaded part increases or decreases depending on the number, and the bell curve moves forward or backward when you change the true mean.

Relevant Application:
Understanding hypothesis testing and type II error is essential to fields like evidence-based medicine, quality engineering, and reliability engineering, among others.

Active Learning Approach:
The variance, hypotheses, and critical values are given. Students can increase or decrease the level of significance (α), true mean (μ), and sample size to see how these
changes affect the other factors involved.

Learn Key Concepts:

  • Examine the interrelationship between α, sample size, and β (the probability of making a type II error).
  • Develop an understanding of the concept of type II errors and the calculation of beta.
  • Explore the relationship between α and β.

 


Are you an instructor who would like to explore these lessons further?

Sign up for FREE student access today!

More simulations, stat!

Remember that in the appendix of your courseware, great resources for student engagement help you bring the real world into your classroom! Check out two examples:

1. Direct Mail Game

In the game, students assume the role of a direct mail marketing manager for a company that markets inexpensive computer software. Their task is to develop a mailing strategy by finding mailing lists that will produce sufficient sales to be profitable.

The game provides an environment in which students apply statistical concepts while making business decisions.

While students can explore the game on their own, we recommend playing it in class.

Dr. Hawkes created this game when he was a statistics professor. He says that this lesson was always his students’ favorite each semester.

A row of lists 1-3 shows each list's price, number, and how many sampled. Below that, the mailing results are displayed, including the list number, cost per name, sample size, number of responses and their data, the mailing costs, the old balance, profit, and new balance. The cash on hand is displayed below, which is $19,968.50.

2. Name That Distribution

Name that Distribution is a concept builder that strengthens analytical skills in distribution recognition and data analysis.

Students view the histogram, frequency, statistics, and sample data of a distribution. They can increase the number of intervals and choose to view a hint if they’re unsure of the answer. As they play with the different options to analyze the data, students combine that information to make an educated guess about the distribution type.

Check out a hint:
A text box called Hints is shown, which more information on uniform distributions. It displays the theoretical variance, and explains how to identify this distribution type.

Below is an example of a distribution type:

A histogram is shown. Below it is the question "What type of distribution is described by the sample?" with the multiple choice options of uniform, normal, exponential, chi-square, Poisson, and mystery. An arrow points to the answer uniform, and another arrow points to a submit button.
Students new to this kind of data analysis will begin to understand how they can apply this knowledge to the many real-world scenarios that they can evaluate through detecting typical or skewed data.


The Direct Mail lesson is available in:

  • Discovering Statistics Appendix A.9
  • Discovering Business Statistics Appendix A.10
  • Beginning Statistics Appendix A.5

The Name that Distribution lesson is available in Appendix A.3 in all three statistics courses.

Minitab’s Blog: A Statistician’s Dream Resource

One of our favorite statistics resources is Minitab’s blog, http://blog.minitab.com/. Here, statisticians have compiled tips, tricks, and how-tos regarding anything stat-related, as well as easy ways to use Minitab.

These posts are great to share in class or assign for homework so students better understand the concepts they’re applying. Students will like them because most posts are short and to the point, include images of the software so they don’t get lost in each step, and make connections to real-world examples of statistics.

One post, How to Compute Probabilities, walks students through using the Minitab software to compute binomial probabilities, create a table of probabilities, and then visualize them. Another post, Five Ways to Make Your Control Charts More Effective, gives audiences a practical, five-step guide to enhancing their control charts, including identifying drifts ASAP and accounting for atypical periods. Michelle Parat’s Statistical Tools for Process Validation series walks readers through process design, process qualification, and continued process verification to show audiences not only how to complete these steps, but to understand how important they are at companies and real-world settings.

Hawkes Learning’s statistics materials can be bundled with Minitab. Just call us at 1-800-426-9538 to learn more about this option!