Unit 8 · Standard 6.SP.4
Display Data: Box Plots
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
A box from Q1 to Q3 with a line at the median, and whiskers from min to max
Box Plot
A graph that shows how data is spread using five key numbers.
Data: 10, 15, 20, 25, 30 → median is 20 (the 3rd value)
Median
The middle number that splits the data in half.
Data: 2, 4, 6, 8, 10, 12, 14 → Q1 = 4 (median of lower half), Q3 = 12 (median of upper half)
Quartile
Numbers that split the data into four equal parts.
If Q1 = 12 and Q3 = 20, then IQR = 20 − 12 = 8 — the middle 50% spans 8 units
Interquartile Range
The spread of the middle half of the data (Q3 − Q1).
A box plot where the median is centered in the box shows symmetric distribution
Data distribution
How the data looks: where it sits and how spread out it is.
Small IQR = low variability in the middle 50%. Large IQR = high variability
Variability
How spread out the numbers are.
Key Ideas & Notes
- The basketball league wants to compare scoring across teams.
- Here are the points scored by each player on the Wildcats in their last game: 4, 6, 8, 10, 12, 14, 15, 18, 22, 24, 28.
- The league needs a quick visual that shows the spread, the middle 50%, and any high or low scorers.
- Time to build a box plot!
Think About It
- What are the lowest and highest scores?
- What score is in the middle of the data?
- Are the scores bunched together or spread out?
My Notes
Guided Examples
Example 1
A box plot shows: Min = 10, Q1 = 15, Median = 20, Q3 = 28, Max = 35. What is the interquartile range (IQR)?
Solution: IQR = Q3 − Q1 = 28 − 15 = 13.
Answer: A. 13
Example 2
On a box plot, what does the line inside the box represent?
Solution: The line inside the box of a box plot always represents the median.
Answer: A. The median
Example 3
What percentage of data falls between Q1 and Q3 on a box plot?
Solution: The box in a box plot contains the middle 50% of the data (from Q1 to Q3).
Answer: A. 50%
Write About the Math The Writing Revolution
I can explain my box plot using the words box plot, median, quartile, and interquartile range.
1. Kernel Sentence subject + verb
Model: Box Plot is a graph that shows how data is spread using five key numbers.Diagrama de caja es una gráfica que muestra cómo se reparten los datos con cinco números clave.
Write a kernel sentence about box plot. Use a subject and a verb.Escribe una oración base sobre diagrama de caja. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Box Plot matters in mathDiagrama de caja importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Box Plot matters in math because ___.Diagrama de caja importa en matemáticas porque ___.
Box Plot matters in math, but ___.Diagrama de caja importa en matemáticas, pero ___.
Box Plot matters in math, so ___.Diagrama de caja importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about box plot.Di un hecho verdadero sobre box plot.
Box plot ___.
Ask a question about box plot.Haz una pregunta sobre box plot.
How does ___ ?¿Cómo ___ ?
Show excitement about box plot.Muestra entusiasmo sobre box plot.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with box plot.Dile a un compañero qué hacer con box plot.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The box shows ___.La caja muestra ___.
The median is ___.La mediana es ___.
I would compare ___ using box plots.Compararía ___ usando diagramas de caja.
Try It
Solve on your own. Check the answer key when you are done.
1. Find the range of: 14, 22, 8, 31, 17
- 23
- 31
- 8
- 18
2. Two box plots show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?
- Team A's middle 50% is more consistent; Team B's is more spread out
- Team B is a better team
- Team A has a higher median
- The IQRs don't tell you about consistency
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Two basketball teams played 9 games each. Team A: 40, 42, 44, 46, 48, 50, 52, 54, 56. Team B: 30, 35, 40, 45, 48, 50, 55, 60, 65. Find the five-number summary and IQR for each team. Which team is more consistent? Which has a wider spread in the middle 50%?
Sentence starter: Team A: Min=___, Q1=___, Median=___, Q3=___, Max=___, IQR=___. Team B: Min=___, Q1=___, Median=___, Q3=___, Max=___, IQR=___. Team ___ is more consistent because its IQR is ___.
Reflect — Exit Ticket
A box plot has Q1 = 20 and Q3 = 36. What is the IQR and what does it represent?
- IQR = 16; it is the spread of the middle 50% of the data
- IQR = 56; it is the total of Q1 and Q3
- IQR = 28; it is the median between Q1 and Q3
- IQR = 36; it is the value of Q3
Answer Key & Teacher Guide
- Try It 1: A. 23 — Range = max − min = 31 − 8 = 23.
- Try It 2: A. Team A's middle 50% is more consistent; Team B's is more spread out — A smaller IQR means the middle 50% of data is more tightly clustered. Team A's scoring is more consistent in the middle range.
- Exit Ticket: A. IQR = 16; it is the spread of the middle 50% of the data — IQR = Q3 − Q1 = 36 − 20 = 16. The IQR tells you the range of the middle 50% of the data.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Box Plot is a graph that shows how data is spread using five key numbers.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).