# Statistically Speaking....

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## Objective

The students will be able to recognize a statistical question as one that anticpates variablility in the data related to the question and accounts for it in the answers.

#### Big Idea

Determining a good statistical question is the foundation of statistics.

## DO NOW

10 minutes

DO NOW:

The beginning part of this lesson sets the students up to start thinking about and predicting what possible responses will come from asking statistical questions. The questions for the do now will be addressed in the 1st scenario on slide one of the power point.

## The Makings of a Good Statistical Question

60 minutes

The first slide of the power point not only introduces the vocabulary, but sets them up to looking at statistical questions that pertain to them in real life.  Read through the slide with the students and have them come up with the definitions for the highlighted words.   Understanding vocabulary will be key to determining a good statistical question.

Next, we will be looking at analyzing sample methods.  Part of asking a good statistical question is to understand the who, where, and the how many.  We will look at two questions together and then they will work in partners to answer two more.

(ACTIVITY:  HUSUPU, stands for Hands up, Stand up, Pair up)  Allow the students to find a partner.  Once a partner is found, have them move to the perimeter of the room (this allows the teacher to stand in the middle to listen to conversations.)  Have the students decide on an A or B or randomly choose who goes first by who is the tallest, who has the longest hair, who has the most siblings. Then when the first person has been chosen, put the question on the board. Instruct both students to read the scenario.  Give enough time to digest the information and formulate a thought.  On your command, have the first person tell their partner which sampling method is best and why.  Once the first person is done, allow the partner to respond by agreeing or disagreeing and why.  When this is done, solicit responses from random partners.

Switch partners and do the same for problem two.

When done, have students return to their seats to look at the next section of the notes.

Identifying potentially biased samples.  In this section, the students will be looking at sample questions and determining if there is bias in the question.  If there is bias, the students can come up with ways to make the question unbiased. For example, changing the location of where the question is be surveyed or changing the amount of people surveyed.  If the question is not bias, they will need to explain why it is not.  When whole class discussion is complete, have the students do a new HUSUPU and find a different partner.  Repeat the activity using new scenario questions.

Finally, the students will be looking at statistical questions to determine if they are random, unbiased and anticipate variability.   If the question is not a good one, they will re-write it.

Repeat the HUSUPU with a new partner and new scenarios.

Scaffolding and Extensions:  The students will be looking at real life scenarios to determine good statistical questions.  Students will be given plenty of opportunity to look at and discuss with tablemates their justifications for whether or not the question is unbiased, random and anticipates variability. Struggling students will benefit from the peer interaction and students that are working to mastery will benefit from higher level thinking involved in justifying their answers.

## Closure

10 minutes

Have the students write down 3 good statistical questions that they will be using to survey their classmates.  Responses will need to be both numerical and categorical and be unbiased, random and anticipate variability.  Have groups of students share their statistical questions and allow their classmates to decide if they are random, unbiased and anticipate variability.  Students can then revise their questioning to support a good statistical questions.

This information can be shared as whole group or collected for evidence of student learning

Addressing common misconceptions:  When coming up with their own statistical question, the students don’t think about how many possible responses they could get.  For example, when asked “what’s your favorite color”, I like to say “can I choose any color I want”?  “Can your classmates choose any color they want”?  Students then realize that there are so many colors available that it’s important to limit the amount of choices made available and their question needs to be more specific.