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.
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.
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.
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.
Build and compare box plots using the five-number summary.
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.
Median
The middle value of a data set when the values are ordered from least to greatest.
Quartile
One of the values that divides an ordered data set into four equal-sized groups.
Lower Extreme
The least value in a data set, shown at the left end of a box plot.
Upper Extreme
The greatest value in a data set, shown at the right end of a box plot.
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.
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.
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.
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.
Materials for the Data Lab.
- A. Number Line Strips
- B. Ruler
- C. Two-Box Comparison Cards
- D. Your Data Journal
- E. A calculator (optional)
Order first, always: no box plot gets built, and no two box plots get compared, before every value is arranged from least to greatest.
Box Plot Comparison Lab
We'll build two box plots from related data sets, then compare what each one reveals.
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.
Data Journal Entry
Accountability Checklist
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.
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