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

Lesson 2.4Represent and Describe Data in a Box Plot

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.

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 2.4Represent and Describe Data in a Box Plot

Version ASupported 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.

Part 1Understand the ideamodels and meaning

1Circle the letter of the best answer. Show how you know.
On a box plot, what does the line inside the box represent?
1. AThe median
2. BThe mean
3. CThe mode
4. DThe range
Hint Picture a box plot: a box with whiskers, and a line cutting through the box. That line marks the CENTER of the data.
Show your work
2Write the name of the correct group on each line.
Order the steps for making a box plot.

Groups: Steps (in order)
- Step 1: Order the data from least to greatest
- Step 2: Find the median (middle value)
- Step 3: Find Q1 (median of the lower half)
- Step 4: Find Q3 (median of the upper half)
- Step 5: Draw the box from Q1 to Q3 with a line at the median, and whiskers to min and max
Hint Always order the data first before finding any measures.

Part 2Apply itreal-world problems

3Circle the letter of the best answer. Show how you know.
A box plot shows: Min = 10, Q1 = 15, Median = 20, Q3 = 28, Max = 35. What is the interquartile range (IQR)?
1. A10
2. B13
3. C20
4. D25
Hint You're given five numbers, but IQR only uses two of them: Q1 and Q3. Ignore the min, median, and max.
Put the data in order

Work
1. 1OrderSmallest to largest.
2. 2CountHow many values?
3. 3LocateMiddle, or add and divide.
4. 4AnswerSay which measure it is.
4Circle the letter of the best answer. Show how you know.
What percentage of data falls between Q1 and Q3 on a box plot?
1. A25%
2. B50%
3. C75%
4. D100%
Hint Quartiles cut the data into 4 equal parts — 'quart' like 'quarter.' Each part holds the same share of the data.
Put the data in order

Work
1. 1OrderSmallest to largest.
2. 2CountHow many values?
3. 3LocateMiddle, or add and divide.
4. 4AnswerSay which measure it is.
5Circle the letter of the best answer. Show how you know.
Find the range of: 14, 22, 8, 31, 17
1. A8
2. B18
3. C23
4. D31
Hint Range = how far the data stretches: the gap between the biggest and smallest values only. The middle values don't matter.
Put the data in order

Work
1. 1OrderSmallest to largest.
2. 2CountHow many values?
3. 3LocateMiddle, or add and divide.
4. 4AnswerSay which measure it is.

Part 3Explain and correctreasoning

6Find the mistake. Explain it, then show the correct work.
The Added-Quartiles IQR Mistake
1. 1Box plot valuesBobcats' box plot: Min = 10, Q1 = 18, Median = 24, Q3 = 30, Max = 40
2. 2GoalFind the interquartile range (IQR).
3. 3Student's workIQR = Q3 + Q1 = 30 + 18 = 48
Which step has the mistake? Explain what went wrong, then show the correct work.

Hint IQR stands for InterQuartile RANGE — a range is found by subtracting, not adding.
Correct work
Correct answer:

Explain your thinkingThe IQR is Q3 − Q1 = 26 − 10 = 16. What does this tell you about the middle 50% of scorers?

Sentence starter The middle 50% of players scored between ___ and ___ points. The IQR of ___ means the middle half of the data is spread across ___ points. This tells me ___.

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

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

Lesson 2.4Represent and Describe Data in a Box Plot

Version BCore 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.

Part 1Understand the ideamodels and meaning

1Complete the table. Show how you found each value.

Complete the table.

Measure Value
Data: 5, 8, 12, 15, 18, 20, 25, 30, 35
Minimum
Q1 (median of lower half: 5, 8, 12, 15)
Median
Q3 (median of upper half: 20, 25, 30, 35)
Maximum
IQR (Q3 − Q1)

Show your work
2Write the letter of the matching item on each line.
Match each box plot term to its meaning.
1. Minimum
2. Q1
3. Median
4. Q3
5. IQR
6. Maximum
- ASmallest value in the data set
- BMedian of the lower half
- CMiddle value of the entire data set
- DMedian of the upper half
- EQ3 − Q1 (spread of middle 50%)
- FLargest value in the data set
3Mark and label each value on the number line.

Data: 3, 5, 7, 9, 11, 13, 15. Place the five-number summary on the number line.
Show your thinking
4Circle the letter of the best answer. Show how you know.
Two box plots show: Team A has IQR = 8, Team B has IQR = 22. What does this tell you?
1. ATeam A's middle 50% is more consistent; Team B's is more spread out
2. BTeam B is a better team
3. CTeam A has a higher median
4. DThe IQRs don't tell you about consistency
Show your work

Measure	Value
Data: 5, 8, 12, 15, 18, 20, 25, 30, 35
Minimum
Q1 (median of lower half: 5, 8, 12, 15)
Median
Q3 (median of upper half: 20, 25, 30, 35)
Maximum
IQR (Q3 − Q1)

Part 2Explain and correctreasoning

5Find the mistake. Explain it, then show the correct work.
The Quartile-Is-One-Value Mistake
1. 1Data (ordered)Eagles' game scores: 4, 8, 10, 14, 18, 22, 26, 30 (8 values)
2. 2MedianWith 8 values, Median = (14 + 18) ÷ 2 = 16 ✓
3. 3Q1Lower half = 4, 8, 10, 14 → Q1 = 10
4. 4Q3Upper half = 18, 22, 26, 30 → Q3 = (22 + 26) ÷ 2 = 24
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:

Explain your thinkingThe IQR is Q3 − Q1 = 26 − 10 = 16. What does this tell you about the middle 50% of scorers?

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

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

Lesson 2.4Represent and Describe Data in a Box Plot

ChallengeExtension

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.

Part 1Understand the ideamodels and meaning

1Write the letter of the matching item on each line.
Match each box plot feature with what it tells you about the data.
1. Long right whisker, short left whisker
2. Median line centered in the box
3. Very small box (small IQR)
4. Very large box (large IQR)
- ASkewed right — some high values stretch far from the box
- BApproximately symmetric in the middle 50%
- CMiddle 50% is tightly clustered — consistent
- DMiddle 50% is widely spread — high variability

Part 2Explain and correctreasoning

2Find the mistake. Explain it, then show the correct work.
Find the Box Plot Error
1. 1Data3, 7, 9, 12, 15, 18, 21
2. 2Min and MaxMin = 3, Max = 21
3. 3MedianMiddle value = 12 ✓
4. 4Q1 and Q3Q1 = 9, Q3 = 18
Which step has the mistake? Explain what went wrong, then show the correct work.

Correct work
Correct answer:
3Answer in complete 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%?
Write your answer

Explain your thinkingThe IQR is Q3 − Q1 = 26 − 10 = 16. What does this tell you about the middle 50% of scorers?

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