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

Lesson 2.42.4 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can make and read a box plot to summarize a data set — one step at a time, with support.

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 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.

  1. Order the values: 58, 61, 64, 66, 71, 77, 83.
  2. Mark the median, 66 — the middle value of the seven.
  3. Lower half 58, 61, 64 gives quartile 1 as 61. Upper half gives quartile 3 as 77.
  4. 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.

  1. Order the seven scores:
  2. Median (the middle score):
  3. Quartile 1 (middle of lower half): Quartile 3 (upper half):
  4. 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 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target With my small group, I can make and read a box plot to summarize a data set — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    0246810121416Data values
    7 values: an odd count.

    Find the five numbers for a box plot of this data: 2, 3, 6, 8, 9, 11, 14. There are 7 values.

    1. 1What is the median, the middle value?
    2. 2The lower half is 2, 3, 6. What is Q1?
    3. 3The upper half is 9, 11, 14. What is Q3?
    4. 4What are the least and greatest values?
    Final answer:
  2. 2Complete each step, then write the final answer.
    02468101214Data values
    6 values: an even count.

    Find the five numbers for a box plot of this data: 2, 4, 6, 7, 11, 13. There are 6 values.

    1. 1There are 6 values. Find the median: (6 + 7) ÷ 2.
    2. 2The lower half is 2, 4, 6. What is Q1?
    3. 3The upper half is 7, 11, 13. What is Q3?
    4. 4What are the least and greatest values?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Here are 7 values in order: 1, 2, 4, 5, 7, 8, 9. What is Q3?

    Show your work

    Hint Find the median first. Q3 is the middle of the values greater than the median.

    Final answer:
  4. 4Complete each step, then write the final answer.

    A team's scores in order are 5, 7, 9, 12, 13, 16, 18, 20, 21, 25, 27. What is Q1?

    Show your work

    Hint There are 11 values. The median is the 6th. Q1 is the middle of the 5 values less than it.

    Final answer:
  5. 5Complete each step, then write the final answer.

    A team scored 10, 14, 6, 18 and 12 points in five games. What is Q3 for a box plot of the scores?

    Show your work

    Hint Put the scores in order first. The upper half has two values.

    Final answer:
  6. 6Complete each step, then write the final answer.

    A box plot shows least 2, Q1 5, median 8, Q3 12, greatest 15. Ava says the box ends at the greatest value. At what number does the box really end on the right?

    Show your work

    Hint The box goes from Q1 to Q3. What goes out to the greatest value?

    Final answer:

Explain your thinkingAfter you find the median, how do you find Q1 and Q3? Use the data 2, 3, 6, 8, 9, 11, 14 to explain.

Sentence starter First I find the median, which is ___. · Q1 is the middle of ___, and Q3 is the middle of ___.

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