## central_tendency_intro.pptx - Section 2: Direct Instruction

*central_tendency_intro.pptx*

*central_tendency_intro.pptx*

# Asking a Statistical Question

Lesson 1 of 19

## Objective: SWBAT write their own statistical question and measure the data they receive using the measures of central tendency.

## Big Idea: It is great when students are able to help develop the content of a lesson. In this lesson, students ask a statistical question that is of interest to them and calculate basic statistical measures on that data.

*37 minutes*

#### Direct Instruction

*15 min*

By now, many of the students have determined that we are going to be learning about statistics.

(1) I ask all the students to do a free-write for 2 minutes about everything they know or have heard of dealing with statistics. Then I ask students to do a **think-pair-share** with their partner. I then call on each pair to share out. We quickly record the answers on the board and if a group has nothing new to add we put a check next to an idea(s) that they had as well. Many students mention the measures of central tendency, types of charts and graphs, many mention that it has something to do with numbers.

(2) Statistics has to do with three things **collection, organization, and analysis **of data. I ask students to take everything in their list and put their words and ideas under one of those three categories. When debriefing this idea we refer back to the opening activity. When all students came in we **collected** the data. We could then **organize** the data by ordering it or by keeping track of the number of 5's and 6's and 7's etc. and make a chart. Lastly we could **analyze** the data by making statements like "most people get 7 hours of sleep."

(3) Next we discuss statistical questions. I ask students to think about why the question they were asked on the way in the door was a statistical question? After students have a few moments to think, I call on a a student to share their thoughts and then on other students to see if they have something to add to what the first student said. We then go through the attributes of a statistical question from the slideshow.

#### Resources

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#### Investigation

*15 min*

In pairs, students make up their own statistical question that they will be able to ask to 10-15 classmates. They travel with their partner around the room gathering their data. While this can be somewhat chaotic, it is important to keep students moving. Before they begin, I explain to the students that each interaction/exchange should take no more then 10-20 seconds. Students will then go back to their seats and with their partner, analyze the data using the four measures of central tendency. After this, students determine how spread out their data is (NOTE: this is a fairly subjective question at this point but I want to get students thinking about whether most of the data is near the center or spread out from the center). Lastly they write a statement about what their measures of central tendency tell them in terms of their question (MP3). They can choose any one of the measures or use multiple measures in their statement.

**Extention/scaffolds: **I like to extend my groups that excel in this lesson by planting the seed regarding the connection between the two measures of center: mean and median. I found in this lesson that many of the data sets that students construct have a mean and median that are close to each other or the same. I ask them how they would have to change the data set in order to effect the mean (MP2)? This question gets them thinking about how the mean is effected by very large or very small members of the data set. This will eventually lead to an understanding of outliers and when the median is a better measure than the mean.

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#### Closure

*5 min*

Students will answer a **ticket out the door** question regarding the four measures of central tendency (see last slide of powerpoint). The information from this ticket out the door will be used to group students for the next day's lesson. This question addresses a foundational understanding of the content. This ticket out is collected as students leave the room for the day.

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- LESSON 1: Asking a Statistical Question
- LESSON 2: Measures of Center
- LESSON 3: Practice with Measures of Central Tendency
- LESSON 4: Organizing Data with a Box Plot
- LESSON 5: Understanding Box Plots (with Assessment)
- LESSON 6: Analyzing a Box Plot
- LESSON 7: Constructing a Histogram
- LESSON 8: Modeling with Box Plots and Histograms
- LESSON 9: Connecting Box Plots and Histograms
- LESSON 10: What's this table saying?
- LESSON 11: Creating Two-Way Tables
- LESSON 12: More with Conditional, Joint, and Marginal Frequencies
- LESSON 13: Using a Scatterplot to Model Data
- LESSON 14: A Bivariate Relationship
- LESSON 15: Scatterplots and Non-Linear Data
- LESSON 16: Modeling with Non-Linear Data
- LESSON 17: Analyzing Residuals
- LESSON 18: Creating a Residual Plot
- LESSON 19: Got Ups? A Statistics Unit Task