Neft Teacher · Notes Packet

Unit 8 · Standard 6.SP.4

Display Data: Box Plots

Lesson 8-5

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

Illustration of Box Plot: A graph that shows how data is spread using five key numbers.

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.

Illustration of Median: The middle number that splits the data in half.

Data: 10, 15, 20, 25, 30 → median is 20 (the 3rd value)

Median

The middle number that splits the data in half.

Illustration of Quartile: Numbers that split the data into four equal parts.

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.

Illustration of Interquartile Range: The spread of the middle half of the data (Q3 − Q1).

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).

Illustration of Data distribution: How the data looks: where it sits and how spread out it is.

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.

Illustration of Variability: How spread out the numbers are.

Small IQR = low variability in the middle 50%. Large IQR = high variability

Variability

How spread out the numbers are.

Key Ideas & Notes

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.

becauseporque

Box Plot matters in math because ___.Diagrama de caja importa en matemáticas porque ___.

butpero

Box Plot matters in math, but ___.Diagrama de caja importa en matemáticas, pero ___.

soentonces

Box Plot matters in math, so ___.Diagrama de caja importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about box plot.Di un hecho verdadero sobre box plot.

Box plot ___.

QuestionPregunta

Ask a question about box plot.Haz una pregunta sobre box plot.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about box plot.Muestra entusiasmo sobre box plot.

Wow, ___ !¡Guau, ___ !

CommandMandato

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

  1. 23
  2. 31
  3. 8
  4. 18
Show your work:

2. Two box plots show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?

  1. Team A's middle 50% is more consistent; Team B's is more spread out
  2. Team B is a better team
  3. Team A has a higher median
  4. The IQRs don't tell you about consistency
Show your work:

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 ___.

Show your work:

Reflect — Exit Ticket

A box plot has Q1 = 20 and Q3 = 36. What is the IQR and what does it represent?

  1. IQR = 16; it is the spread of the middle 50% of the data
  2. IQR = 56; it is the total of Q1 and Q3
  3. IQR = 28; it is the median between Q1 and Q3
  4. IQR = 36; it is the value of Q3
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 23 — Range = max − min = 31 − 8 = 23.
  2. 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.
  3. 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