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.

Why This Matters 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!

Start hereWords for this lesson

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

WordWhat it meansExample
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 example

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

Times (min): 14, 5, 20, 9, 23, 11, 16.

  1. Order: 5, 9, 11, 14, 16, 20, 23. Median = 14.
  2. Lower half 5, 9, 11: Q1 = 9. Upper half 16, 20, 23: Q3 = 20.
  3. Box from 9 to 20, line at 14, whiskers to 5 and 23.

Answer: 5, 9, 14, 20, 23

Now you trySame steps, your turn

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

New, smaller data set: 2, 5, 5, 8, 11. First, what is the median (the middle value)?

Answer:

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 out!A 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

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

Level 0Most support · every hint printed

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.

Why This Matters 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!

How it worksWorked example

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

Times (min): 14, 5, 20, 9, 23, 11, 16.

  1. Order: 5, 9, 11, 14, 16, 20, 23. Median = 14.
  2. Lower half 5, 9, 11: Q1 = 9. Upper half 16, 20, 23: Q3 = 20.
  3. Box from 9 to 20, line at 14, whiskers to 5 and 23.

Answer: 5, 9, 14, 20, 23

Part 1Understand the ideamodels and meaning
  1. 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
    Steps to try
    1. Picture a box plot: a box with whiskers, and a line cutting through the box. That line marks the CENTER of the data.
    2. The box runs from Q1 to Q3, so the line inside splits the middle 50% in half. Think about which measure splits ordered data into halves.
    3. First step: recall which measure means 'the middle value of the ordered data.' The line inside the box always marks that exact measure.
    Show your work
Part 2Apply itreal-world problems
  1. 2Circle 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
    Steps to try
    1. You're given five numbers, but IQR only uses two of them: Q1 and Q3. Ignore the min, median, and max.
    2. IQR = Q3 − Q1. Find Q3 (28) and Q1 (15) in the summary — the IQR is their difference, the width of the box.
    3. Set up the subtraction Q3 − Q1: that's 28 − 15. The difference you get is the IQR.
    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.
  2. 3Circle 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%
    Steps to try
    1. Quartiles cut the data into 4 equal parts — 'quart' like 'quarter.' Each part holds the same share of the data.
    2. Each quarter of the data is 25%. Count how many quarters sit between Q1 and Q3: Q1 to the median, then the median to Q3.
    3. First step: Q1 to the median is one quarter — 25%. Add the quarter from the median up to Q3 to get the box's total share.
    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.
  3. 4Circle the letter of the best answer. Show how you know.

    Find the range of: 14, 22, 8, 31, 17

    1. A8
    2. B39
    3. C23
    4. D31
    Steps to try
    1. Range = how far the data stretches: the gap between the biggest and smallest values only. The middle values don't matter.
    2. Scan the list 14, 22, 8, 31, 17: find the maximum and the minimum, then subtract the min from the max.
    3. First step: the max is 31 and the min is 8. Set up 31 − 8 — that difference is the range.
    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.

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 ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help