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

Lesson 2.10Choose Appropriate Measures

Set B · Version ASecond form · supported practice

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

Learning target I can choose the best measure of center for a data set based on its shape.

Why This Matters The students want to describe the data they collected about the number of years of teaching experience of the teachers in their school. Which measure of center and measure of variation should they use to summarize the data set?

RememberChoose Appropriate Measures

Choosing Appropriate Measures of Center & Spread The mean and the median both describe the center of a data set, but one fits better depending on the shape. When the data has an outlier (a value far from the rest), the median is usually the better choice.

  1. Symmetric Data (No Outliers): Use Mean and MAD.
  2. Skewed Data (Has Outliers): Use Median and IQR (outliers distort the mean).
  3. Compare distributions using both center (typical value) and spread (variability)

Words: Mean (Media)Median (Mediana)Outlier (Valor atípico)Skewed (Sesgado)Data distribution (Distribución de datos)

  1. 1Circle the letter of the best answer. Show how you know.

    The mean of a data set is 20. A value is 26. What is the absolute deviation?

    1. A−6
    2. B6
    3. C26
    4. D46
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

    1. A−4
    2. B4
    3. C11
    4. D26
    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?

    1. A1
    2. B3
    3. C5
    4. D15
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    Team A has MAD = 2.1 points. Team B has MAD = 6.8 points. Which team is more consistent?

    1. ATeam B — higher MAD means better performance
    2. BBoth are equally consistent
    3. CCannot tell from MAD alone
    4. DTeam A — lower MAD means scores are closer to the mean
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    A sports reporter writes: 'The average ticket price for the playoffs is $85.' The actual prices are: $45, $50, $48, $52, $55, $260. The $260 ticket is a courtside seat. What is the mean ticket price?

    1. A$50
    2. B$51
    3. C$85
    4. D$260
    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.
  6. 6Circle the letter of the best answer. Show how you know.

    A sports reporter writes: 'The average ticket price for the playoffs is $85.' The actual prices are: $45, $50, $48, $52, $55, $260. The $260 ticket is a courtside seat. What is the median ticket price?

    1. A$50
    2. B$51
    3. C$52
    4. D$85
    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 ___.

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

Lesson 2.10Choose Appropriate Measures

Set B · Version BSecond form · core practice

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

Learning target I can choose the best measure of center for a data set based on its shape.

Why This Matters The students want to describe the data they collected about the number of years of teaching experience of the teachers in their school. Which measure of center and measure of variation should they use to summarize the data set?

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each scouting question to the measure that answers it.

    1. What was a typical game when one score is a record-breaking outlier?
    2. Which shoe size do most players wear?
    3. On a symmetric, outlier-free set, what is the average score?
    4. How far apart are the highest and lowest sprint times?
    • AMedian
    • BMode
    • CMean
    • DRange
  2. 2Write the name of the correct group on each line.

    Sort each measure into whether it describes the CENTER of the data or the SPREAD of the data.

    Groups: Measure of Center Measure of Spread
    • Mean
    • Median
    • Mode
    • Range
    • Mean absolute deviation (MAD)
Part 2Apply itreal-world problems
  1. 3Circle the letter of the best answer. Show how you know.

    A sports reporter writes: 'The average ticket price for the playoffs is $85.' The actual prices are: $45, $50, $48, $52, $55, $260. The $260 ticket is a courtside seat. Which measure better describes a 'typical' ticket?

    1. AThe median, because the $260 outlier pulls the mean far above most prices
    2. BThe mean, because it uses every value
    3. CNeither — you should use the mode
    4. DThe mean, because $85 is between the extremes
    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A scout records points per game: 14, 16, 15, 17, 16, 58. To report a TYPICAL game, which measure of center is best?

    1. AMean, because it uses every game
    2. BRange, because it shows the highest game
    3. CMedian, because 58 is an outlier that pulls the mean up
    4. DMode, because 16 appears twice
    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    The equipment manager needs to order the MOST COMMON jersey size from this list: M, L, M, S, M, L, M. Which measure answers the question?

    1. AMean, because it averages the sizes
    2. BMedian, because it finds the middle size
    3. CMode, because it names the value that appears most
    4. DRange, because it shows the size gap
    Show your work
  4. 6Circle the letter of the best answer. Show how you know.

    A coach wants to know how SPREAD OUT the team's free-throw makes are: 6, 7, 6, 8, 18. Which measure of spread is most affected by the lone 18?

    1. ARange, because it is the highest minus the lowest value
    2. BMedian, because it is in the middle
    3. CMode, because it is the most common
    4. DMean absolute deviation only, never the range
    Show your work

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

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