Objectives for this activity
During this activity, you will:
- Identify some key elements of statistical thinking.
- Describe the importance of statistical literacy.
Statistics vs. Mathematics – What Is the Difference?
This class is a community of learners. Having shared goals strengthens communities. Our shared goal for this course is to maximize the learning experience for everyone. Therefore, while you’ll have plenty of time for individual thought, much of the work in the course is done collaboratively, where you will work in pairs or small groups to discuss, plan, and execute activities in the curriculum. Engaging in these activities will help you become a critical thinker and provide you with a space to share and learn from each other’s experiences.
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In this activity, you’ll explore some major differences between statistical thinking and mathematical thinking and begin to understand the statistical process as an investigative process. Along the way, you’ll begin to discover some of the aspects of building a positive learning community. Keep in mind that our shared goal for this course is to maximize the learning experience for everyone.
The Need for Statistics
We live in a data-driven society. We are surrounded by data on a daily basis. In our personal lives as consumers, citizens, and professionals, it is important that we are able to interpret the information we receive to make sound decisions. Knowledge of statistical tools and processes empowers us to feel comfortable making quantitative decisions in our careers and in matters that affect quality of life issues, and enables us to weigh for ourselves statistical claims made in the media. The study that you’ll do in this course will provide a foundation for your statistical literacy.
Let’s begin by developing an understanding of the need for statistics. First, watch the video below individually and make some notes for yourself regarding why we study statistics. Type your notes in answer to Question 1. Afterward, you’ll form groups to answer the remaining questions.
Question 1
Record your notes regarding why we study statistics as you watched the video Why Statistics?
Guidance
[Intro: ” Did you find the video interesting? One of the key points showed how analyzing statistics is like a microscope that allows us to see things that are too big for our eyes to take in. It allows us to take a big thing and shrink it down to something small so that we can see it. We’ll never really be able to comprehend the vast complexities of a really large set of data. Trying to gain that kind of perspective is immediately overwhelming. Statistics gives us tools to analyze tendencies, trends, likelihoods, and associations. Let’s work together in groups to explore this idea. In your groups, you’ll need people to play certain roles to help you work together efficiently. So, after a brief exchange of names and career pathways, decide who will serve in which roles.]
Forming Groups
Next, you will work in groups to complete the following questions. Quickly introduce yourselves to the members in your group by telling them your first and last name, along with your desired career pathway. You’ll need a minimum of three people to serve in the group roles of note-taker, reporter, and timekeeper. If you have more people, you may consider adding the roles of moderator and listener. You may find that some members naturally tend to act as moderators and listeners. If so, value that tendency and take advantage of it! Here’s a brief description of all the roles:
- Note-taker (required) – takes notes.
- Reporter (required) – reports the result to the class.
- Timekeeper (required) – manages times and keeps team members on track.
- Moderator (optional)– directs activity and helps to keep the group on task.
- Listener (optional) – extracts the ideas from the brainstorming or group activity and recaps them; offers explanations and reasoning.
Let’s try practice group work now by answering Question 2 below.
question 2
In the video, one of the statisticians from the United Statistics Bureau discussed how analyzing statistics is like a microscope that allows us to see things that are just too big for our eyes to take in. Let’s continue to explore this idea. Parts A and B below ask you to perform unrelated tasks. Answer these questions individually.
Part A: Use the table below to record estimates of the number of hours of sleep you were able to get for each night.
| Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
Part B: Write 293 in expanded notation.
Now come together as a group to compare and discuss your answers to Parts A and B. Record the results in answer to Part C below.
Part C: Compare your answers for Parts A and B with the other members in your group. Discuss how they are the same, how they are different, and possible reasons why they are the same or different.
In Part A, the information you recorded in the table are data! The sleep times are not all the same, as they changed from person to person and even from night to night. You also may have identified some reasons that impacted the amount of sleep each student was able to get each night. You discovered that the data varied from student to student. It is highly probable that there were no students who had the exact same answers in their tables.
Answer part D as a group now, based on the ideas you developed above.
Part D: Consider the number of movies college students watch during freshmen year. If you asked 100 freshmen on your campus this question, do you expect to get the exact same answer for each student?
Question 3
In statistics, we want to ask investigative questions. Consider the questions below together and record your answers. Your answers may vary, so discuss them to arrive at a consensus to answer each question.
Part A: Do you think you would find any studies on the number of hearts that humans have?
Part B: What is an investigative question that you could ask regarding the data you recorded in Question 2, Part A?
Part C: What additional information would you need to collect if you wanted to know why college students do not get enough sleep each night?
Question 4
Identify at least one difference between mathematics and statistics.
An Investigative Process
The statistical process is an investigative process. It is also a repetitive or cyclical process. Analyzing the results of one study can often lead researchers to consider other research questions and then conduct additional research. Thinking more carefully about how the data were collected may also lead researchers to consider ways to improve the data collection process.
A particular research topic is at the heart of any statistical investigation. The data collected for the research objective have context within a story that statistics helps us understand. The research objective presents a scenario that helps us get to the context of the data that needs to be collected to tell that story. And, since data vary, one goal of the process is to determine the source of the variability. We see that the questions, data collection, and analysis surrounding the research objective are integral and inseparable parts of the process.
In summary, we understand that the statistics process is an investigative process that revolves around a research objective. It involves asking questions, collecting the appropriate data, then analyzing the data and interpreting results.
Question 5
Complete the following diagram to illustrate the statistical process.
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Some of the key takeaways from this activity include that:
- Statistical thinking is different from mathematical thinking.
- Data will vary, within an individual or within a group.
- The context of the data is important. Researchers must consider the goals of the study and what the data represent.
- Working together as a learning community offers many benefits. Let’s begin establishing our own learning community in this course.
Now let’s put it all together to answer Question 6 below: the reasons why we use statistics, the importance of understanding how it works, and nature of statistical thinking.
question 6
Why do you think statistics and statistical literacy are important?
