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# Introduction to Statistics

Lesson 1 of 13

## Objective: SWBAT understand that statistics is the science of learning from data. They can explain how understanding statistics will help them make sense of the world around them.

#### Overview of Statistics

*10 min*

To hook my students on the importance of statistics, I show them a few interesting statistical displays. I select some graphics related to events currently in the news and others that I tend to use from semester to semester. One of my favorites is the Health and Wealth of Nations display from Gapminder, which is a creative display of four variables using motion.

After presenting and discussing these graphics, I lead a discussion about the **definition of statistics**. I do a big statistics sales pitch at this point because I feel strongly that the math my students learn in our study of statistics is some of the most useful material they will learn in high school.

#### Resources

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#### Student Survey

*20 min*

So that we have a data set to come back to at various points in our study of statistics, I ask my students to fill out a survey like the one linked here (or as Anonymous Statistics Survey.pdf at right):

http://bit.ly/samplestatsurvey

I am careful to ask students some questions with categorical responses like "what color hair do you have?" and others with quantitative responses like "how many hours of sleep did you get last night?" Other variables like "birthdate" will generate discussion about how the variable type is not always determined by whether the values it takes are numbers or text.

From our class data set, my students will be able to explore distributions of single variables as well as correlations between two variables. I have found that students generally enjoy using data about themselves – especially if I include some funny variables like "how many outfits did you try on this morning?" or "what % of the time do you text when you visit the restroom?"

I use a Google form for this survey for a couple of reasons. First, my students can respond to the survey using any device. Most will use their cell phone or an ipod, but they could use a personal or school laptop or tablet as well. Second, when everyone has answered the survey, I can alter the settings of the document so that students have access to the class results.

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#### Group Data Exploration

*40 min*

After my students have submitted their Google Forms to answer the survey, I provide them with a link to the class results. I ask students to arrange themselves in groups of 3 and take one laptop per group from the cart so they can access our data set.

For the next 40 minutes, these groups will select and explore either a one- or two-variable data set from our class data. This is a very open-ended assignment and I prepare my students for it by discussing it directly. I make it clear that THEY choose whether to examine a single variable or the relationship between two variables; THEY decide what questions to answer about the data; THEY select the most appropriate display that will help their classmates understand the data. I tell my students that I am not quite sure how much they know about statistics and part of what I hope to learn from the day's activity is where they are in their understanding of statistics.

I ask my students to use the following protocol in completing the group work [**MP3**]:

- Look at the data you have selected and determine at least 3 questions you think your classmates might have about it
- Create a graphical display that helps your classmates understand the data
- Answer the questions you developed in Step 1
- Be prepared to present your findings to the class (taking about 3 minutes to do so)

Students work in their groups for 40 minutes. During this time I set the overhead timer so that they know how much time they have left to get their presentation ready. Although I circulate around the room to listen to their conversations and determine how much they know about statistics, I do not provide much guidance at this point. I want my students to learn to ask questions of themselves and each other and this is a good time for them to practice that [**MP3**].

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#### Group Data Presentations

*20 min*

In order to move through the presentations efficiently, I order the groups by passing out numbers while they work. Because I have been listening in on their discussions, I am able to choose an order that will make the presentations go more smoothly. For example, if two groups chose the same variable with different types of displays, I might put them back to back. If one group had a particularly weak presentation, I might have them present first or second.

Each group of students comes to the front of the room with their posters and presents their findings to the class. [MP3, MP6] I encourage questions from the audience after each presentation.

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#### Wrap-Up and Assignment

*10 min*

After the presentations, I bring the group back together for a wrap-up. I point out interesting features of the presentations and begin using some of the statistics terms that students will learn in the unit (categorical and quantitative data, individuals, variables, etc). I explain that the evening's homework, WS Descriptive Stats Vocabulary is a packet that introduces 12 really important terms. I expect that the homework will take my students about 45 minutes to finish.

#### Resources

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- LESSON 1: Introduction to Statistics
- LESSON 2: Looking at One-Variable Data Sets
- LESSON 3: Describing Single-Variable Data Sets
- LESSON 4: One-Variable Distribution Activity
- LESSON 5: Bell-Shaped Distributions and the Normal Model
- LESSON 6: Quiz on Distributions and the Empirical Rule
- LESSON 7: Using Technology with Normal Model
- LESSON 8: Assessing Statistical Significance DAY 1
- LESSON 9: Assessing Statistical Significance DAY 2
- LESSON 10: Developing Confidence Intervals DAY 1
- LESSON 11: Developing Confidence Intervals DAY 2
- LESSON 12: Review of One-Variable Statistics
- LESSON 13: Unit Assessment: One-Variable Statistics