Box Plots on the Job | The Center for Quantitative Studies | Studio Aletheia
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Box Plots on the Job

Lesson 07 · Application, Create Box Plots

Data analysts use box plots to settle real arguments, which product is more reliable, which store performs better, which route is faster. Today you'll build box plots for a real workplace comparison and write up what they prove.

Focus Box plots for real comparisons
Accountability Data Journal + Exit Ticket
Indicator Create box plots representing a numerical data set using ...
The Center for Quantitative Studies Color Palette Aletheian Green · Aletheian Gold
Learning Targets

Learning Targets and Success Criteria

In the workplace, a box plot isn't just a diagram, it's evidence for a decision.

Targets

What I will learn

  • I can build box plots from real workplace-style data sets.
  • I can compare two box plots to support a business decision.
  • I can explain what a data analyst would conclude from a pair of box plots.
  • I can write a short recommendation based on box plot evidence.
Success Criteria

What success looks like

  • I build an accurate box plot for a real-world data set.
  • I use median and spread to compare two box plots correctly.
  • I state a clear conclusion that the box plots actually support.
  • I write a recommendation that a real decision-maker could use.
Standard 6.DPSR.1.2

Use box plots to compare data and support a real decision.

6.DPSR.1.2 — Create box plots representing a numerical data set using the five-number summary (lower extreme, first quartile, median, third quartile, upper extreme).
Vocabulary

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.

01 · Order

Median

The middle value of a data set when the values are ordered from least to greatest.

02 · Identify

Quartile

One of the values that divides an ordered data set into four equal-sized groups.

03 · Identify

Lower Extreme

The least value in a data set, shown at the left end of a box plot.

04 · Identify

Upper Extreme

The greatest value in a data set, shown at the right end of a box plot.

05 · Represent

Box Plot

A diagram that displays a numerical data set using five key values: the lowest number, first quartile, median, third quartile, and highest number.

College & Career Connections

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.

Data Analyst

Which Delivery Route Is More Reliable?

A delivery company tracks delivery times for two routes. Route A's box plot has a median of 25 minutes with a narrow box; Route B's has a median of 22 minutes but a much wider box, including some very long delivery days. A data analyst would recommend Route A for reliability, even though its typical time is a bit slower, because customers hate surprises more than a few extra minutes.

Data Scientist

Comparing Two Product Versions

Before launching an app update, a data scientist compares how long the old version and the new version take to load, using box plots built from thousands of load times. A box plot with a lower median and a narrower spread tells the team the new version isn't just faster on average, it's also more consistently fast, which matters just as much to real users.

Mini-Lesson

Box Plots Make the Case

In the workplace, a box plot isn't just a diagram, it's evidence for a decision.

Imagine a company comparing two delivery routes. For each route, someone orders the data, finds the medianThe middle value of a data set when the values are ordered from least to greatest. delivery time, the lower extremeThe least value in a data set, shown at the left end of a box plot. and upper extremeThe greatest value in a data set, shown at the right end of a box plot. times, and each quartileOne of the values that divides an ordered data set into four equal-sized groups. in between. Turning those five numbers into a box plotA diagram that displays a numerical data set using five key values: the lowest number, first quartile, median, third quartile, and highest number. for each route lets the whole team see, instantly, which route is typically faster and which route is more predictable.

That's the real power of a box plot at work: it turns a spreadsheet full of numbers into a picture a manager can read in five seconds, and it separates two different questions, what's typical (the median) and how consistent things are (the spread), that a single average could never answer on its own.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.

Check for Understanding · CFU 1
Route A has a median delivery time of 25 minutes and a narrow box. Route B has a median of 22 minutes and a wide box. As a data analyst, which route would you recommend to a manager who values reliability, and why?
Toolkit

Materials for the Data Lab.

  • A. Workplace Data Set Cards
  • B. Number Line Strips
  • C. Ruler
  • D. Your Data Journal
  • E. A calculator (optional)
Non-negotiable routine

Order first, always: no box plot gets built, and no business conclusion gets written, before every value is arranged from least to greatest.

Guided Practice

Data Analyst Comparison Lab

You'll build box plots for a real workplace scenario and use them to make a recommendation.

Data Lab
Each scenario below compares two real-world options using small numerical data sets.
1 · Order
Order both data sets in your chosen workplace scenario.
2 · Identify
Identify the five-number summary for both options.
3 · Describe
Describe what each box plot would show about typical value and spread.
4 · Question
Write the recommendation question a manager would actually want answered.
Hands-On

Write a Box Plot Recommendation

You'll build both box plots and write the recommendation a data analyst would hand to a manager.

1
Order: Order both data sets in your chosen workplace scenario.
2
Summarize: Find the five-number summary for each option.
3
Draw: Draw both box plots on the same number line.
4
Recommend: Write a 2-3 sentence recommendation using the medians and spread as evidence.
Required

Data Journal Entry

Which Mathematical Process Standard did you rely on most today — Problem Solving, Connections, Representation & Communication, Analyze & Justify, or Structure & Patterns? Give one specific example from your Data Lab or hands-on work.
Checklist

Accountability Checklist

Required · Exit Challenge

Make the Call

Machine A's box plot has a median of 2 defects and a narrow box. Machine B's has a median of 1 defect but a wide box reaching up to 9. Which machine would you recommend keeping, and why? Use the five-number summary in your answer.

Lesson 07 · Application, Create Box Plots

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