Pre-Algebra Lesson
Reading the Game: Comparing Data Sets Using Box Plots
Shared by A STEM Educator
7th GradeUniversal Design for Learning50 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 ]
🏀 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.'
🏊 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.'
3Task 3
DEVELOPING — STUDENT CHOICE OF SPORTS CONTEXT
🏅 YOUR CHOICE: Pick the sport that interests you most. All four data sets have the same structure — choose the one that feels most relevant to you.
I chose sport: _______________
Task: Without a step-by-step scaffold this time, find the five-number summary and IQR for your chosen data set. Then draw a complete, labeled box plot on graph paper or on the digital number line in Desmos.
[DESMOS OPTION: You can verify your box plot by entering your data into a Desmos table and using the built-in statistics tools.]
After drawing your box plot, write one sentence explaining what the IQR tells a sports fan about this athlete's or team's performance.
🏅 YOUR CHOICE: Pick the sport that interests you most. All four data sets have the same structure — choose the one that feels most relevant to you.
| Letter | Sport | Data set |
|---|---|---|
| A | 🏈 Football | Yards gained by a running back in 10 carries: 3, 12, 0, 8, 22, 5, 14, 9, 18, 7 |
| B | ⚽ Soccer | Shots on goal per game over 10 games: 6, 2, 9, 4, 11, 7, 3, 9, 5, 8 |
| C | 🏃 Track | 400m race times (seconds) for 10 races: 58, 63, 55, 61, 70, 57, 64, 59, 66, 62 |
| D | 🏐 Volleyball | Points scored per set over 10 sets: 18, 25, 21, 14, 25, 22, 19, 25, 17, 23 |
I chose sport: _______________
Task: Without a step-by-step scaffold this time, find the five-number summary and IQR for your chosen data set. Then draw a complete, labeled box plot on graph paper or on the digital number line in Desmos.
[DESMOS OPTION: You can verify your box plot by entering your data into a Desmos table and using the built-in statistics tools.]
After drawing your box plot, write one sentence explaining what the IQR tells a sports fan about this athlete's or team's performance.
4Task 4
DEVELOPING — READING A BOX PLOT
🎽 SPORTS CONTEXT: The box plot below shows the number of points scored by a high school basketball team across a full 18-game season.
[ Interactive graph / diagram, available in the full lesson ]
Using ONLY the box plot above (no raw data), answer the following questions:
1. What is the median number of points scored? ___
2. What is the range of points scored this season? Show your work:
Range = ___ − ___ = ___
3. What is the IQR? Show your work:
IQR = ___ − ___ = ___
4. In what range of values did the MIDDLE 50% of games fall? Between ___ and ___ points.
5. The team's coach says, 'We were pretty consistent — most of our scores stayed close together.' Do the statistics support this claim? Circle one: YES / NO / PARTIALLY
Explain using at least ONE number from the box plot:
_______________________________________________
[SENTENCE STARTER for Question 5: 'The IQR of ___ points means that the middle 50% of games had scores within a ___ -point range, which suggests the team was ___ consistent because...']
[EXTENSION: If a game score of 41 points were added to the data, would it likely be an outlier? How could you check? (Hint: Outlier rule: below Q1 − 1.5×IQR or above Q3 + 1.5×IQR)]
🎽 SPORTS CONTEXT: The box plot below shows the number of points scored by a high school basketball team across a full 18-game season.
[ Interactive graph / diagram, available in the full lesson ]
Using ONLY the box plot above (no raw data), answer the following questions:
1. What is the median number of points scored? ___
2. What is the range of points scored this season? Show your work:
Range = ___ − ___ = ___
3. What is the IQR? Show your work:
IQR = ___ − ___ = ___
4. In what range of values did the MIDDLE 50% of games fall? Between ___ and ___ points.
5. The team's coach says, 'We were pretty consistent — most of our scores stayed close together.' Do the statistics support this claim? Circle one: YES / NO / PARTIALLY
Explain using at least ONE number from the box plot:
_______________________________________________
[SENTENCE STARTER for Question 5: 'The IQR of ___ points means that the middle 50% of games had scores within a ___ -point range, which suggests the team was ___ consistent because...']
[EXTENSION: If a game score of 41 points were added to the data, would it likely be an outlier? How could you check? (Hint: Outlier rule: below Q1 − 1.5×IQR or above Q3 + 1.5×IQR)]
5Task 5
🏀 SPORTS CONTEXT: Two middle school basketball players — Jordan and Alex — both played 15 games this season. Their points-per-game distributions are shown in the double box plot below.
[ Interactive graph / diagram, available in the full lesson ]
Use the double box plot to complete the comparison table below:
Now answer these comparison questions using your table:
1. Who has the higher MEDIAN score? What does this tell you about typical performance?
2. Who has the larger RANGE? What does this tell you about consistency?
3. Who has the larger IQR? What does this tell you about the spread of the MIDDLE 50% of their games?
4. Their coach needs to pick ONE player to be the team's primary scorer in a championship game where consistency is the top priority. Based ONLY on the statistics, who would you recommend and why?
[SENTENCE STARTER: 'I would recommend ___ because their IQR of ___ is ___ than ___'s IQR of ___, which means their middle 50% of scores are ___ spread out, indicating ___ consistency.']
[ Interactive graph / diagram, available in the full lesson ]
Use the double box plot to complete the comparison table below:
| Statistical Measure | Jordan | Alex |
|---|---|---|
| Minimum | ||
| Q1 | ||
| Median | ||
| Q3 | ||
| Maximum | ||
| Range | ||
| IQR |
Now answer these comparison questions using your table:
1. Who has the higher MEDIAN score? What does this tell you about typical performance?
2. Who has the larger RANGE? What does this tell you about consistency?
3. Who has the larger IQR? What does this tell you about the spread of the MIDDLE 50% of their games?
4. Their coach needs to pick ONE player to be the team's primary scorer in a championship game where consistency is the top priority. Based ONLY on the statistics, who would you recommend and why?
[SENTENCE STARTER: 'I would recommend ___ because their IQR of ___ is ___ than ___'s IQR of ___, which means their middle 50% of scores are ___ spread out, indicating ___ consistency.']
6Task 6
EXPERT CHOICE — CEILING (Part 1 of 2)
🌍 SPORTS CONTEXT: A sports journalist is writing a story comparing two rival track teams — the Northside Rockets and the Southside Eagles — based on their 100-meter dash times (in seconds) from a full season of meets.
Northside Rockets times (12 meets):
11.2, 10.8, 12.1, 11.5, 10.6, 11.9, 12.3, 11.0, 10.9, 11.7, 12.0, 11.3
Southside Eagles times (12 meets):
11.8, 11.4, 12.5, 11.6, 11.9, 12.2, 11.5, 11.7, 12.0, 11.3, 11.8, 12.1
[REMINDER: In track, LOWER times are BETTER — a faster runner finishes in fewer seconds.]
YOUR TASK:
1. Find the five-number summary and IQR for BOTH teams. Show all work.
2. Construct a double box plot comparing both teams on a single number line. Choose your format:
□ Hand-drawn on graph paper (ruler required)
□ Digital in Desmos
□ Using the printed box plot manipulative cutouts
Label all five values on each box plot. Use a different color for each team.
You will use these box plots in Task 7 to write your full analysis.
🌍 SPORTS CONTEXT: A sports journalist is writing a story comparing two rival track teams — the Northside Rockets and the Southside Eagles — based on their 100-meter dash times (in seconds) from a full season of meets.
Northside Rockets times (12 meets):
11.2, 10.8, 12.1, 11.5, 10.6, 11.9, 12.3, 11.0, 10.9, 11.7, 12.0, 11.3
Southside Eagles times (12 meets):
11.8, 11.4, 12.5, 11.6, 11.9, 12.2, 11.5, 11.7, 12.0, 11.3, 11.8, 12.1
[REMINDER: In track, LOWER times are BETTER — a faster runner finishes in fewer seconds.]
YOUR TASK:
1. Find the five-number summary and IQR for BOTH teams. Show all work.
2. Construct a double box plot comparing both teams on a single number line. Choose your format:
□ Hand-drawn on graph paper (ruler required)
□ Digital in Desmos
□ Using the printed box plot manipulative cutouts
Label all five values on each box plot. Use a different color for each team.
You will use these box plots in Task 7 to write your full analysis.
7Task 7
EXPERT CHOICE — CEILING (Part 2 of 2)
📰 SPORTS CONTEXT: You are the sports journalist. Using your double box plot from Task 6, write your full analysis comparing the Northside Rockets and Southside Eagles.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
CHOOSE YOUR RESPONSE MODALITY:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
□ OPTION A — WRITTEN ANALYSIS (Journalist Mode)
Write a 3–5 sentence sports article paragraph comparing the two teams. You MUST include:
• Both teams' medians (and what they mean in context)
• Both teams' IQRs (and what they mean about consistency)
• A clear conclusion about which team is faster AND which team is more consistent
• At least 4 statistical vocabulary words: median, IQR, range, spread, quartile, distribution
□ OPTION B — ANNOTATED DIAGRAM (Analyst Mode)
Create a fully annotated version of your double box plot. Add:
• Arrows and labels pointing to key features with written explanations
• A comparison callout box noting: 'Team ___ has a lower median, meaning...'
• A consistency callout box noting: 'Team ___ has a smaller IQR, meaning...'
• A 'Bottom Line' box with your final conclusion
• Minimum 6 annotations total
□ OPTION C — VERBAL EXPLANATION (Broadcaster Mode)
Record a 60–90 second voice memo OR deliver a live explanation to your teacher acting as 'the coach.' Your explanation must cover:
• What the median tells you about each team's typical performance
• What the IQR tells you about each team's consistency
• Which team you would predict to win a championship meet and why
• Use at least 3 statistical vocabulary words naturally in your explanation
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
ALL OPTIONS must answer this inference question:
'Based on the data, which team would you predict to perform better in a championship meet where every second counts? Justify your answer with specific statistics.'
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
[CHALLENGE EXTENSION: Is there any overlap between the two teams' boxes? What does overlapping IQR ranges tell us about the certainty of our prediction?]
📰 SPORTS CONTEXT: You are the sports journalist. Using your double box plot from Task 6, write your full analysis comparing the Northside Rockets and Southside Eagles.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
CHOOSE YOUR RESPONSE MODALITY:
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
□ OPTION A — WRITTEN ANALYSIS (Journalist Mode)
Write a 3–5 sentence sports article paragraph comparing the two teams. You MUST include:
• Both teams' medians (and what they mean in context)
• Both teams' IQRs (and what they mean about consistency)
• A clear conclusion about which team is faster AND which team is more consistent
• At least 4 statistical vocabulary words: median, IQR, range, spread, quartile, distribution
□ OPTION B — ANNOTATED DIAGRAM (Analyst Mode)
Create a fully annotated version of your double box plot. Add:
• Arrows and labels pointing to key features with written explanations
• A comparison callout box noting: 'Team ___ has a lower median, meaning...'
• A consistency callout box noting: 'Team ___ has a smaller IQR, meaning...'
• A 'Bottom Line' box with your final conclusion
• Minimum 6 annotations total
□ OPTION C — VERBAL EXPLANATION (Broadcaster Mode)
Record a 60–90 second voice memo OR deliver a live explanation to your teacher acting as 'the coach.' Your explanation must cover:
• What the median tells you about each team's typical performance
• What the IQR tells you about each team's consistency
• Which team you would predict to win a championship meet and why
• Use at least 3 statistical vocabulary words naturally in your explanation
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
ALL OPTIONS must answer this inference question:
'Based on the data, which team would you predict to perform better in a championship meet where every second counts? Justify your answer with specific statistics.'
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
[CHALLENGE EXTENSION: Is there any overlap between the two teams' boxes? What does overlapping IQR ranges tell us about the certainty of our prediction?]
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