Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.52.2 · 2.4 · 2.5 · 2.10 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 2.2 · 2.4 · 2.5 · 2.10 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

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

WordWhat it meansExample
Display Data with HistogramsSpanish: Representar datos con histogramas Group numerical data into intervals and show each interval's frequency with a bar. Each touching bar shows how many values fall in one interval.
HistogramSpanish: Histograma A bar graph that groups data into equal ranges. The bars touch. Bars side by side: 0-9 pts (3 players), 10-19 pts (8 players), 20-29 pts (4 players)
FrequencySpanish: Frecuencia How many times a value shows up. If 5 players scored 10-19 points, the frequency for that interval is 5
IntervalSpanish: Intervalo A range of numbers used to group data. 0-9, 10-19, 20-29 are intervals of width 10 — each covers 10 values
DistributionSpanish: Distribución How the data is spread out. Most data in the middle with fewer at the ends = bell-shaped; most on one side with a tail = skewed
VariabilitySpanish: Variabilidad How spread out the numbers are. Close together or far apart

How it worksWorked examplefinding the range and the iqr

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

Seven history test scores are 74, 90, 83, 68, 86, 77, 94. Find the range and the IQR.

  1. Order the values: 68, 74, 77, 83, 86, 90, 94.
  2. Range: take the least value away from the greatest value. That gives 26 points.
  3. The median is 83, so quartile 1 is 74 and quartile 3 is 90.
  4. IQR: take quartile 1 away from quartile 3. That gives 16 points.

Answer: The range is 26 points and the interquartile range is 16 points.

Now you trySame steps, your turn

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

Seven delivery times in minutes are 31, 45, 28, 52, 37, 41, 34. Find the range and the IQR.

  1. Order the values:
  2. Greatest: Least: Range: minutes
  3. Quartile 1: Quartile 3:
  4. Subtract quartile 1 from quartile 3. IQR: minutes
Answer:range and IQR in minutes

Say it and write itSentence starters

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

  • The greatest value is and the least value is .
  • The range is , which describes .
  • Quartile 1 is and quartile 3 is , so the IQR is .
  • The IQR describes only of the data.

Word bank rangeinterquartile rangequartilespreadvariabilitygreatestleastsubtractmiddle halfextremeorderconsistent

Watch outA common mistake

A common mistake in Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present. For example, given a player's points per game 14, 16, 15, 17, 16, 58, a student calculates the mean (136 ÷ 6 ≈ 22.7) and reports that as the typical game — but 58 is far from the cluster of 14–17, so it pulls the mean above 5 of the 6 games. The median (16) actually represents a typical game here. Before choosing a measure, always scan the data for an outlier or a long tail first: only use the mean once you've confirmed the data has neither.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.DS.3

Lesson 2.52.2 · 2.4 · 2.5 · 2.10 Catch-Up

Catch-UpSkill bridge

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

Learning target I can show I am caught up on Lessons 2.2 · 2.4 · 2.5 · 2.10 by using each lesson's big idea in mixed practice.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 2.2) In a histogram, what does the height of each bar represent?

    1. AThe average of the data in that interval
    2. BThe frequency (count) of data in that interval
    3. CThe range of the interval
    4. DThe median of the data

    Hint Think about what you'd count to draw one bar: you'd tally how many data values land inside that interval.

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 2.4) On a box plot, what does the line inside the box represent?

    1. AThe mean
    2. BThe median
    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
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    (Lesson 2.2) A histogram shows these frequencies: 0–4: 3 players, 5–9: 8 players, 10–14: 12 players, 15–19: 5 players. How many players are represented in total?

    1. A12
    2. B15
    3. C20
    4. D28

    Hint The question asks for the TOTAL across all four intervals — not the tallest bar and not the biggest interval.
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 4Circle the letter of the best answer. Show how you know.

    (Lesson 2.4) 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.
  3. 5Circle the letter of the best answer. Show how you know.

    (Lesson 2.5) A data set runs from a least value of 12 to a greatest value of 30. What is the range?

    1. A12
    2. B18
    3. C21
    4. D30

    Hint Range asks how far it is from one end of the data to the other.

    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 thinkingWhat pattern do you notice about when median is the better choice?

Sentence starter The median is better when the data has ___ because the mean gets pulled toward ___. The mean is better when the data is ___ because ___.

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