Describe Data by Range and Interquartile Range
I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.
How to Use This Deck
Click Present or press F11 for fullscreen. Use arrow keys to advance.
Blue boxes show exactly what to say, ask, and how long to spend.
Text boxes, polls, and drag-sort save automatically in the browser.
Press N or click 📝 in the toolbar for pacing tips and answers.
Launch the full HTML activity for independent practice.
File → Print or the print button for handout copies.
🎯 Content Objective / Objetivo de contenido
I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Two classes have the same median score, 81. Can you tell which class did better? What else would you need to know?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Spread Detective
The league analyst is comparing two sixth-grade classes that took the same math test. Both classes have the SAME median score, 81 — so the medians alone cannot tell them apart. Your job is to measure how spread out each class's scores are, using the range and the interquartile range, and decide which class did better overall.
Concept Launch
💡 How spread out is the data?
A measure of center like the median tells you where the data sits. It does not tell you how far apart the values are. Two classes can share the same median and still look nothing alike. Range and interquartile range are the two numbers that describe that spread.
Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Range and Interquartile Range Rango y rango intercuartílico |
Two numbers that describe spread: the range covers all the data, and the interquartile range covers only the middle half. Dos números que describen la dispersión: el rango cubre todos los datos y el rango intercuartílico solo la mitad central. |
Range 26 covers 68 to 94; IQR 12.5 covers only 75.5 to 88 | |
| Range Rango |
The distance from the least value to the greatest value, found by subtracting: greatest − least. La distancia del valor menor al mayor, que se halla restando: mayor − menor. |
94 − 68 = 26 | |
| Quartile Cuartil |
One of the three values that cut an ordered data set into four equal-sized groups. Uno de los tres valores que dividen un conjunto ordenado de datos en cuatro grupos del mismo tamaño. |
Q1 = 75.5, median = 83.5, Q3 = 88 | |
| Interquartile range Rango intercuartílico |
The distance across the middle half of the data, found by subtracting the first quartile from the third: Q3 − Q1. La distancia a lo largo de la mitad central de los datos: se resta el primer cuartil del tercero: Q3 − Q1. |
88 − 75.5 = 12.5 — the width of the box on a box plot | |
| Variability Variabilidad |
How much the values in a data set differ from one another — whether they sit close together or far apart. Cuánto se diferencian entre sí los valores de un conjunto de datos: si están juntos o muy separados. |
Close together = low variability; spread apart = high variability | |
| Measure of variation Medida de variación |
A single number that describes the spread of a whole data set. The range and the IQR are both measures of variation. Un solo número que describe la dispersión de todo un conjunto de datos. El rango y el RIC son medidas de variación. |
One number stands in for the spread of all 20 scores |
Which Word Fits?
The range uses the ___ values; the interquartile range uses the ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Two classes have the same median score, 81. Can you tell which class did better? What else would you need to know?
👂 Listen For
Students name a measure of spread rather than another measure of center.
Extend: Could two classes have the same median AND the same range and still look different?
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Each statement describes a spread. Sort it under the measure that produced it.
✍️ Explore Discourse
Both numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
Why does the range change a lot when one unusual value is added, but the IQR barely moves?
👂 Listen For
Students point at WHICH values each measure subtracts, not just at the results.
Extend: Which measure would you report to a coach after a record-breaking game, and why?
Practice Check A
A box plot shows: least 68, Q1 75.5, median 83.5, Q3 88, greatest 94. What are the range and the IQR?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Team A's salaries have a range of $14M and an IQR of $7M. Team B's have a range of $7M and an IQR of $2.5M. Both teams have the same median salary. What does this tell a player?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Statistical vs Not Sort
Drag each question into the correct column.
✍️ Justify Your Thinking
Sort each label into the correct box.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability" — and it works because ___.
Because Range and Interquartile Range means ___, but a tricky part is ___, so I have to ___.
A common mistake with Range and Interquartile Range is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Range to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability because ___
Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability but ___
Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Fill in the table using today's strategy.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A data set runs from a least value of 12 to a greatest value of 30. What is the range?
A box plot shows: least 68, Q1 75.5, median 83.5, Q3 88, greatest 94. What are the range and the IQR?
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
Two sixth-grade classes took the same math test. Class A's box plot reads least 62, Q1 74, median 81, Q3 87, greatest 90. Class B's reads least 70, Q1 76, median 81, Q3 84, greatest 90. Both classes have a median of 81, so the median alone cannot tell you which class did better overall.
✍️ Connection Reasoning
Which class scored better overall, and how do the range and the IQR show it?
Class A's range is ___ and Class B's range is ___, so Class A's scores are more ___. Class A's IQR is ___ and Class B's IQR is ___, so the middle half of Class B is packed into a ___ stretch of points. Because 75% of Class B scored ___ or more, Class B did better ___.
Turn & Talk — Connect
Class A's IQR is 13 and Class B's is 8. Say what that means in the context of the test, not just in numbers.
👂 Listen For
Students translate the number into students and points, not just 'smaller'.
Extend: Does a smaller IQR always mean a class did better?
Summarize: Describe Data by Range and Interquartile Range
Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A box plot has Q1 = 20 and Q3 = 36, with a least value of 10 and a greatest value of 50. What is the IQR, and what does it tell you?
Bonus Exit Check
A data set runs from a least value of 12 to a greatest value of 30. What is the range?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students name a measure of spread rather than another measure of center.
• Students point at WHICH values each measure subtracts, not just at the results.
• Students translate the number into students and points, not just 'smaller'.
• Both definitions are stated as subtractions, with the correct values named.
Common mistake: A common mistake with Range and Interquartile Range is adding the two quartiles instead of subtracting them — writing IQR = Q3 + Q1. With Q1 = 42 and Q3 = 58 that gives 100, which is larger than the data set's entire range of 20. Every measure of variation is a DIFFERENCE, and the IQR can never exceed the range, because the middle half is part of the whole span. If your IQR comes out bigger than your range, you added when you should have subtracted.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: Range 26, IQR 12.5 — Range = 94 − 68 = 26. IQR = 88 − 75.5 = 12.5. The range covers the whole span; the IQR covers only the box.
✓ Practice 2: Team B's salaries cluster much more tightly around the median — Both measures of variation are smaller for Team B, so its salaries vary less: a typical player is more likely to earn close to the median. Team A spreads much wider in both directions.
✓ Practice 3: 18 — Range = greatest − least = 30 − 12 = 18.
✓ Practice 4: 16 — IQR = Q3 − Q1 = 36 − 20 = 16.
✓ Exit ticket: IQR = 16; the middle half of the data spans 16 units — IQR = Q3 − Q1 = 36 − 20 = 16. Because it runs from Q1 to Q3, it describes only the middle half of the values — the width of the box.