Studio Aletheia · The Center for Quantitative Studies
6.DPSR.1.3SC 6th Grade Math
Choosing Center Like an Analyst
Lesson 10 · Application, Choose Median or Mode
A misleading "typical" number has caused real companies real trouble. Today you'll play data analyst, spot the shape and outliers in a workplace data set, and choose the measure of center that tells the truth.
Learning Targets and Success Criteria
Choosing the wrong measure of center isn't just a math mistake, it can mislead a real decision.
What I will learn
- I can identify the shape and outliers in a real workplace data set.
- I can choose the measure of center that best represents the data for a report.
- I can explain how choosing the wrong measure of center could mislead a decision.
- I can write a short data note recommending a measure of center.
What success looks like
- I correctly identify shape and outliers in a workplace-style data set.
- I choose median or mode and justify the choice with evidence from the data.
- I explain a specific way the wrong choice could mislead a real decision.
- I write a clear, evidence-based data note.
Choose the measure of center that reports a data set honestly.
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.
One Outlier Salary Skews the Story
A small company reports employee salaries of 40, 42, 45, 48, and 250 thousand dollars, the last one belonging to the owner. Reporting a measure of center pulled toward that outlier would make salaries look far higher than what almost every employee actually earns, so a careful data analyst chooses the measure that reflects the typical worker's pay honestly.
Two Peaks in Customer Ages
A streaming app finds its users cluster into two age groups, tweens and their parents, a bimodal shape. A data scientist reporting a single middle-of-the-road center number would hide both real audiences, so instead they report the two clusters directly, which helps the marketing team design content for each group instead of guessing at a nonexistent "average" viewer.
The Number That Tells the Truth
Choosing the wrong measure of center isn't just a math mistake, it can mislead a real decision.
Imagine a small business reporting typical employee pay: 40, 42, 45, 48, 250, in thousands of dollars. That last value is an outlierA data value that is much greater or much less than the rest of the values in a data set., and it makes the distribution strongly skewA distribution shape where most of the data bunches on one side and a tail stretches out toward the other side.ed. If the company reported a measure of center pulled toward that outlier, new hires might expect pay that almost nobody near the bottom actually receives. A careful analyst instead reports the value that best reflects what a typical employee earns.
Not every workplace data set is skewed, some are symmetricA distribution shape where the data is evenly balanced on both sides of the center., some are spread uniformA distribution shape where the data values are spread out fairly evenly across the range, with no clear peak.ly with no peak, and some are bimodalA distribution shape with two separate peaks, meaning the data clusters around two different values., clustering around two very different groups, like customer ages split between tweens and their parents. In every case, the analyst's job is the same: look at the shape, watch for outliers, and choose the measure of center that reports the data honestly, not the one that happens to look the most impressive.
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. Workplace Data Set Cards
- B. Data Note Template
- C. Sticky notes
- D. Your Data Journal
- E. A calculator (optional)
Order the data, picture its shape, and check for an outlier before ever recommending a measure of center in a report.
Data Analyst Shape Lab
You'll analyze a real workplace data set and recommend the measure of center you'd put in a report.
Write a Data Note
You'll write a short data note, the kind an analyst attaches to a report, recommending a measure of center.
Data Journal Entry
Accountability Checklist
Write the Honest Number
A company's customer ages are 10, 11, 45, 46, 47. Identify the shape of this distribution and recommend median or mode as the more appropriate description of center for a company report. Explain your reasoning.
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