Box Plots in Action | The Center for Quantitative Studies | Studio Aletheia
The Center for Quantitative Studies spinning orb Studio Aletheia · The Center for Quantitative Studies 6.DPSR.1.2SC 6th Grade Math

Box Plots in Action

Lesson 06 · Guided Practice, Create Box Plots

You built one box plot from scratch yesterday. Today you'll build several, faster and more confidently, and start reading two box plots side-by-side to compare what they show.

Focus Building and comparing box plots
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

Building a box plot gets faster with practice; reading two of them side-by-side is today's new skill.

Targets

What I will learn

  • I can find the five-number summary for multiple data sets accurately and efficiently.
  • I can build a box plot for any small numerical data set.
  • I can compare two box plots by looking at their medians and their spread.
  • I can explain what a wider or narrower box tells me about a data set.
Success Criteria

What success looks like

  • I find each five-number summary correctly without re-checking every step.
  • I build an accurate box plot for at least two different data sets today.
  • I compare two box plots and describe at least one similarity and one difference.
  • I explain the meaning of a wide box versus a narrow box in my own words.
Standard 6.DPSR.1.2

Build and compare box plots using the five-number summary.

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 / Data Scientist

Two Boxes, One Fast Comparison

Soon you'll see analysts put two box plots on the same number line to compare, say, wait times at two stores, in seconds. A wider box, or a median that sits in a different spot, can settle an argument that a table of raw numbers would take minutes to untangle.

Mini-Lesson

Reading Two Boxes at Once

Building a box plot gets faster with practice; reading two of them side-by-side is today's new skill.

You already know the drill: order the data, find the medianThe middle value of a data set when the values are ordered from least to greatest., split into halves, find each quartileOne of the values that divides an ordered data set into four equal-sized groups., then mark 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.. 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. turns those five numbers into a picture, and pictures are easiest to understand when you compare two at once.

Picture two box plots on the same number line, one for Class A's quiz scores and one for Class B's. If Class A's box sits farther to the right, its median score is higher. If Class B's box is wider, its scores are more spread out, less consistent, than Class A's tighter box. You can compare center by comparing medians, and compare consistency by comparing how wide each box and its whiskers stretch, all without ever looking at a single raw number.

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
Team 1's box plot has a median of 14 and a narrow box. Team 2's box plot has a median of 10 and a wide box. Which team scored more consistently, and which team had the higher typical score? Explain using the box plots.
Toolkit

Materials for the Data Lab.

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

Order first, always: no box plot gets built, and no two box plots get compared, before every value is arranged from least to greatest.

Guided Practice

Box Plot Comparison Lab

We'll build two box plots from related data sets, then compare what each one reveals.

Data Lab
Each pair below represents two similar groups, ready to be summarized and compared as box plots.
1 · Order
Order both data sets in your chosen pair from least to greatest.
2 · Identify
Identify the five-number summary for both data sets.
3 · Describe
Describe how the two box plots would compare in median and spread.
4 · Question
Write one question the comparison raises that you'd want to investigate further.
Hands-On

Build and Compare Two Box Plots

You'll draw two box plots on the same number line and write a comparison, like a real data report.

1
Order: Order both data sets in your chosen pair from least to greatest.
2
Summarize: Find the five-number summary for each data set.
3
Draw: Draw both box plots on the same number line, one above the other.
4
Compare: Write 2-3 sentences comparing the medians and the spread of the two box plots.
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

Which Box Tells the Better Story?

Class X's box plot has a median of 82 and a narrow box. Class Y's has a median of 78 and a wide box. Which class had more consistent scores, and which had the higher typical score? Explain using both box plots.

Lesson 06 · Guided Practice, Create Box Plots

The Center for Quantitative Studies · Course Navigation

Move between lessons or return to the larger Studio Aletheia ecosystem.