Studio Aletheia · The Center for Quantitative Studies
6.DPSR.1.3SC 6th Grade Math
Shape, Outliers, and Center
Lesson 09 · Guided Practice, Choose Median or Mode
You can already name a shape and spot an outlier. Today you'll face trickier data sets, ones where the shape isn't obvious at first glance, and defend your measure-of-center choice against a partner's challenge.
Learning Targets and Success Criteria
A quick recap, then the harder cases, where an outlier hides in the middle of ordinary-looking data.
What I will learn
- I can name the shape of a data distribution even when it isn't obvious at first glance.
- I can identify an outlier and explain how it affects the data's shape.
- I can defend a choice of median or mode using specific evidence from the data.
- I can respond to a challenge to my reasoning and revise it if needed.
What success looks like
- I correctly name shape for data sets that require closer inspection.
- I explain how a specific outlier changes a distribution's shape or its measure of center.
- I defend my median-or-mode choice with evidence, not just a guess.
- I revise my reasoning when a partner raises a fair challenge.
Defend a median or mode choice using shape and outlier evidence.
The words we'll use in today's lesson.
These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.
Symmetric
A distribution shape where the data is evenly balanced on both sides of the center.
Skew
A distribution shape where most of the data bunches on one side and a tail stretches out toward the other side.
Uniform
A distribution shape where the data values are spread out fairly evenly across the range, with no clear peak.
Bimodal
A distribution shape with two separate peaks, meaning the data clusters around two different values.
Outlier
A data value that is much greater or much less than the rest of the values in a data set.
Where this shows up in the real world.
Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.
Defending the Number in a Meeting
A data analyst doesn't just pick a measure of center, they get asked to defend it in front of people who disagree. Practicing how to justify median over mode, or the reverse, using the actual shape of the data is exactly the skill that makes an analyst's report convincing instead of just asserted.
When the Shape Isn't Obvious
A quick recap, then the harder cases, where an outlier hides in the middle of ordinary-looking data.
You already know four shapes: symmetricA distribution shape where the data is evenly balanced on both sides of the center., skewA distribution shape where most of the data bunches on one side and a tail stretches out toward the other side.ed, uniformA distribution shape where the data values are spread out fairly evenly across the range, with no clear peak., and bimodalA distribution shape with two separate peaks, meaning the data clusters around two different values.. The tricky part is that real data rarely announces its shape clearly, sometimes you have to order the values and picture the dots carefully before the pattern shows up. An outlierA data value that is much greater or much less than the rest of the values in a data set. can be especially sneaky: a data set of 8, 9, 9, 10, 40 looks almost symmetric among its first four values, until that 40 reveals a strong skew.
Today, when you choose median or mode, you'll need to do more than name your choice, you'll need to defend it against a partner who might disagree. A strong defense points to specific evidence: "I chose median because the 40 is an outlier that would distort other measures," is far more convincing than "I just think median is better."
Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.
Materials for the Data Lab.
- A. Shape Challenge Cards
- B. Partner Debate Sentence Starters
- C. Sticky notes
- D. Your Data Journal
- E. A calculator (optional)
Order the data, picture its shape, and check for an outlier before ever choosing a measure of center, then be ready to defend it.
Defend Your Center Lab
You'll choose a measure of center, then a partner will challenge it, and you'll respond with evidence.
Defend Your Choice
You'll pick a measure of center for a tricky data set, then defend it against a partner's challenge in writing.
Data Journal Entry
Accountability Checklist
Defend It in Writing
A data set is 20, 21, 21, 22, 60. A classmate claims the mode best describes the center. Do you agree? Use the data's shape and its outlier to defend your own choice of median or mode.
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