Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.42.4 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can make and read a box plot to summarize a data set, explain what each part stands for, and build one for a situation I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

Word	What it means	Example
Box PlotSpanish: Diagrama de caja	A graph that shows how data is spread using five key numbers.	Box with two whiskers
MedianSpanish: Mediana	The middle number when you put them in order.	Data: 10, 15, 20, 25, 30 → median is 20 (the 3rd value)
QuartileSpanish: Cuartil	Numbers that split the data into four equal parts.	Q1, median, Q3
Interquartile RangeSpanish: Rango intercuartílico	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
Data distributionSpanish: Distribución de datos	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
VariabilitySpanish: Variabilidad	How spread out the numbers are.	Small IQR = low variability in the middle 50%. Large IQR = high variability

How it worksWorked examplefinding the five-number summary

These numbers are not on your problems. The steps are. Follow them with your own numbers.

Seven daily high temperatures in degrees are 58, 71, 64, 83, 66, 77, 61. Build the box plot.

Order the values: 58, 61, 64, 66, 71, 77, 83.
Mark the median, 66 — the middle value of the seven.
Lower half 58, 61, 64 gives quartile 1 as 61. Upper half gives quartile 3 as 77.
Draw a box from 61 to 77 with a line at 66, then whiskers out to 58 and to 83.

Answer: Five-number summary: 58, 61, 66, 77, 83. The box covers the middle half of the data.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Seven test scores are 42, 55, 36, 48, 39, 52, 45. Build the five-number summary.

Order the seven scores:
Median (the middle score):
Quartile 1 (middle of lower half): Quartile 3 (upper half):
Draw the box from to with a line at , plus both whiskers.

Answer:five-number summary

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

In order the values are .
The median is , so the lower half is .
Quartile 1 is and quartile 3 is .
The box stretches from to , which holds of the data.

Word bank box plotquartilemedianminimummaximumwhiskerboxorderlower halfupper halfmiddlespread

Watch outA common mistake

A common mistake in Display Data: Box Plots is treating a quartile as just one data point instead of the median of a half — for the lower half 4, 8, 10, 14, some students pick 10 (the last value) as Q1 instead of finding the median of that half: Q1 = (8 + 10) ÷ 2 = 9. A second common slip is finding IQR by adding the quartiles instead of subtracting, writing IQR = Q3 + Q1 (like 30 + 18 = 48) instead of IQR = Q3 − Q1 (30 − 18 = 12) — always order the data first, then subtract Q1 from Q3 to find the spread of the middle 50%.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.5

Lesson 2.42.4 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can make and read a box plot to summarize a data set, explain what each part stands for, and build one for a situation I have not seen before.

Part 1Understand the ideamodels and meaning

1Circle the letter of the best answer. Show how you know.
Team A's box plot has Q1 20 and Q3 30. Team B's has Q1 15 and Q3 40. Each team has 20 players. Which statement is true?
1. ABoth boxes hold about 10 players.
2. BTeam B's box holds more players because it is wider.
3. CTeam A's box holds more players because it is shorter.
4. DYou cannot tell how many players are in either box.
Show your work

Part 2Apply itreal-world problems

2Complete each step, then write the final answer.
10 values: an even count.
Find the five numbers for a box plot of this data: 4, 5, 7, 9, 10, 12, 14, 15, 18, 21. There are 10 values.
1. 1Find the median of the 10 values.
2. 2The lower half is 4, 5, 7, 9, 10. What is Q1?
3. 3Find Q3, the middle of the upper half.
4. 4What are the least and greatest values?
Final answer:
3Complete each step, then write the final answer.
Jump distances in inches
A box plot shows the jumps of 40 students in inches: least 30, Q1 42, median 48, Q3 55, greatest 70. About how many students jumped from 42 to 55 inches?
1. 1Which part of the box plot goes from 42 to 55?
2. 2The box holds half the data. About how many students is that?
3. 3About how many students jumped more than 55 inches?
4. 4The right whisker is long. Why does it hold only about 10 students?
Final answer:
4Complete each step, then write the final answer.

Here are 7 values in order: 1.5, 2, 3.5, 4, 5, 6.5, 8. What is Q3?
Show your work
Final answer:
5Complete each step, then write the final answer.

Eight values in order are 2, 4, 6, 9, 11, ?, 16, 20. Q3 is 15. Find the missing value.
Show your work
Final answer:
6Complete each step, then write the final answer.

Video game prices in dollars
A box plot shows the prices of 24 video games: least $10, Q1 $20, median $30, Q3 $45, greatest $60. About how many games cost $30 or less?
Show your work
Final answer:

Explain your thinkingIn the jump box plot, the right whisker is longer than the box. Which part holds more students? Defend your answer.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help