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Pre-Algebra Lesson

Reading the Game: Comparing Data Sets Using Box Plots

Shared by A STEM Educator

7th Gradeudl50 min
Learning Objective

Students will be able to construct and interpret box plots by identifying the median, quartiles, and range of a data set, and will compare two box plots to draw statistically justified inferences about populations — demonstrated through student-chosen modalities including written analysis, verbal explanation, or visual annotation.

Lesson Overview

Students explore how statisticians and sports analysts use box plots to summarize and compare data sets, focusing on median, quartiles, interquartile range, and overall spread. Through a sports context, students move from finding basic measures of center and spread to drawing evidence-based inferences by comparing two box plots.

Materials

  • Printed or digital task sheets (PDF and Google Slides versions available)
  • Colored pencils or markers (at least 2 colors per student)
  • Number line strips (pre-printed, laminated reusable versions for tactile learners)
  • Sticky notes (for kinesthetic sorting activity in Task 1)
  • Rulers
  • Desmos graphing calculator (desmos.com — free, browser-based)
  • Anchor chart: 'Anatomy of a Box Plot' (teacher-prepared, posted visibly)
  • Vocabulary card set: median, quartile, IQR, range, spread, outlier (bilingual English/Spanish version available)
  • Optional: mini whiteboards and dry-erase markers for live response
  • Optional: printed box plot manipulative cutouts for kinesthetic Task 2 variation
  • Headphones (for students using text-to-speech or audio support tools)
  • Graph paper

Scaffolded Task Progression

1Task 1
GUIDED ACCESS — FLOOR

🏀 SPORTS CONTEXT: A scout is tracking how many points a middle school basketball player scored in 9 games this season.

Game scores: 8, 15, 21, 13, 19, 7, 21, 11, 16

Your job is to find the FIVE KEY VALUES that describe this data set. These five values are the building blocks of a box plot.

────────────────────────────────
STEP-BY-STEP SCAFFOLD
────────────────────────────────

STEP 1 — Order the data from least to greatest:
___ , ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___

[KINESTHETIC OPTION: Write each score on a sticky note. Arrange the sticky notes in order on your number line strip. Take a photo or copy the order.]

STEP 2 — Find the MEDIAN (middle value):
With 9 values, the median is the ___th value.
Median = ___

STEP 3 — Find the LOWER HALF (values below the median):
Lower half: ___ , ___ , ___ , ___
The median of the lower half is called the LOWER QUARTILE (Q1).
Q1 = ___

STEP 4 — Find the UPPER HALF (values above the median):
Upper half: ___ , ___ , ___ , ___
The median of the upper half is called the UPPER QUARTILE (Q3).
Q3 = ___

STEP 5 — Record your FIVE-NUMBER SUMMARY:
• Minimum (Min): ___
• Lower Quartile (Q1): ___
• Median (Q2): ___
• Upper Quartile (Q3): ___
• Maximum (Max): ___

STEP 6 — Calculate the RANGE and IQR:
• Range = Max − Min = ___ − ___ = ___
• IQR (Interquartile Range) = Q3 − Q1 = ___ − ___ = ___

[VOCABULARY SUPPORT: Use your vocabulary card for 'quartile,' 'median,' 'IQR,' and 'range' if needed.]

────────────────────────────────
REFERENCE — Anatomy of a Box Plot:
────────────────────────────────

[ Interactive graph / diagram — available in the full lesson ]
2Task 2
GUIDED ACCESS — FLOOR

🏊 SPORTS CONTEXT: A swim coach recorded the finish times (in seconds) for 8 swimmers in a 100-meter freestyle race.

Times: 68, 74, 59, 81, 63, 74, 70, 77

Part A — Complete the Five-Number Summary:
Use the steps from Task 1 as your guide.

Ordered data: ___ , ___ , ___ , ___ , ___ , ___ , ___ , ___

[NOTE: This data set has 8 values — an even number. To find the median of an even data set, average the two middle values.]

Median = (___ + ___) ÷ 2 = ___

Five-Number Summary:
• Min: ___
• Q1: ___
• Median: ___
• Q3: ___
• Max: ___

Range = ___ IQR = ___

Part B — Plot it!
Using your five-number summary, draw a box plot on the number line below. Label each of the five key values.


[ Interactive graph / diagram — available in the full lesson ]


Part C — Interpret:
Complete this sentence using your data:
'The middle 50% of swimmers finished between ___ seconds and ___ seconds, a spread of ___ seconds.'

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