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

Lesson 2.10Choose Appropriate Measures

Start hereWords, worked example, and sentence starters

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?

Start hereWords for this lesson

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

WordWhat it meansExample
MeanSpanish: Media The average. Add all the numbers, then divide by how many there are. Mean of 10, 20, 30 = (10+20+30) ÷ 3 = 20
MedianSpanish: Mediana The middle number when you put them in order. Data: 5, 8, 12, 15, 20 → median is 12 (the 3rd of 5 values)
OutlierSpanish: Valor atípico A number that is much bigger or smaller than the rest. 2, 3, 4, 32 → 32
SkewedSpanish: Sesgado When most data sits on one side with a tail on the other. A long tail to the right
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. Symmetric = even on both sides. Skewed = bunched on one side with a tail
VariabilitySpanish: Variabilidad How spread out the numbers are. 88, 90, 89, 91 (low variability) vs. 50, 70, 95, 100 (high variability)

How it worksWorked example

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

Five friends saved $6, $7, $8, $9 and $50. Which center describes a typical friend?

  1. 50 is an outlier.
  2. Median = 8. Mean = 80 ÷ 5 = 16, more than four of the five values.
  3. The median is closer to most of the values.

Answer: The median, $8

Now you trySame steps, your turn

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

Data set A: 4, 5, 6, 7, 8. Are there any outliers? If not, which measure should we use, mean or median?

Answer:

Say it and write itSentence starters

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

  • The outlier in this set is because .
  • The median is and the mean is .
  • The mean is pulled because .
  • I would report the because .

Word bank outlierskewedclustergapmedianmeantypicalcenterpulledsymmetricdescribedata set

Watch out!A 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

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

Lesson 2.10Choose Appropriate Measures

Version ASupported 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 data description with the best measure of center.

    1. Test scores: 88, 90, 85, 92, 87 (no outliers)
    2. Salaries: $30K, $32K, $35K, $31K, $250K
    3. Race times: 12.1s, 12.3s, 12.0s, 12.2s, 12.1s
    4. Goals scored: 1, 2, 1, 0, 2, 1, 15
    • AMean
    • BMedian
    • CMean
    • DMedian

    Hint Scan each data list for a value that's wildly different from its neighbors — like one huge salary or one giant goal count.

  2. 2Write the name of the correct group on each line.

    Sort each feature by which measure of center it supports.

    Groups: Use Mean Use Median
    • No outliers in the data
    • Data is symmetric
    • All values are close together
    • Data has one or more outliers
    • Data is skewed to one side
    • One extreme value pulls the average

    Hint The mean is sensitive to extreme values — outliers pull it up or down.

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

    A gymnast's scores are: 8.5, 8.8, 8.7, 8.6, 8.9. There are no outliers. Which measure best represents a typical score?

    1. AMedian
    2. BNeither — the data is too small
    3. CMode — the scores are close together
    4. DMean

    Hint Look at the scores: 8.5 up to 8.9 — all five are bunched tightly together with no unusual value.

    Show your work
  2. 4Circle the letter of the best answer. Show how you know.

    A runner's mile times are: 7:10, 7:15, 7:12, 7:20, 12:00. The 12:00 was due to a cramp. Which measure best represents a typical mile?

    1. AMean — it uses all the data
    2. BMedian — the outlier 12:00 pulls the mean too high
    3. CMode — it shows the most common time
    4. DNeither measure works

    Hint Four times are near 7 minutes; one is 12:00 from a cramp. That 12:00 is an outlier, not a typical mile.

    Show your work
  3. 5Circle the letter of the best answer. Show how you know.

    Data set: 5, 6, 7, 7, 8, 50. The mean is about 13.8 and the median is 7. Which better represents the typical value?

    1. AMean (13.8) — it includes all values
    2. BBoth are equally good
    3. CMedian (7) — the outlier 50 inflates the mean
    4. DNeither works for this data

    Hint Five of the six values are between 5 and 8 — then there's 50. Notice where the mean (13.8) lands compared to those five.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Mistake — Forgetting to Order the Data

    1. 1DataA swimmer's lap counts: 9, 12, 8, 11, 10 (no outliers).
    2. 2Find the medianThe student keeps the numbers as written (9, 12, 8, 11, 10) and picks the middle one: median = 8.
    3. 3Choose a measureThe student reports the median (8) as the typical lap count.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint The median is the MIDDLE value only after the numbers are sorted from least to greatest.

    Correct work
    Correct answer:

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

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

    Complete the table.

    Data SetMeanMedianOutlier?Best Measure
    15, 18, 16, 17, 15
    15, 18, 16, 17, 72
    Show your work
  2. 2Write the letter of the matching item on each line.

    Match the reason with whether to use mean or median.

    1. Data is symmetric and has no extreme values
    2. Data has one or more outliers
    3. Data is skewed to one side
    4. All values are clustered close together
    • AUse Mean
    • BUse Median
    • CUse Median
    • DUse Mean
  3. 3Mark and label each value on the number line.

    Data: 10, 12, 11, 13, 50. Place the mean (19.2) and median (12) on the number line. Notice how far apart they are because of the outlier.

    510152025303540455055
    Show your thinking
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A baseball player's batting averages over 6 seasons are: .280, .295, .290, .285, .300, .110. The .110 was an injury-shortened season. Which measure better represents the player's typical batting average?

    1. AMedian, because the .110 outlier pulls the mean down
    2. BMean, because it uses all the data
    3. CMean, because .110 is a real season
    4. DNeither measure works
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Mistake — Choosing the Mean Despite an Outlier

    1. 1DataA receiver's catches per game: 12, 14, 13, 15, 11, 60 (the 60 was a record-setting playoff game).
    2. 2Find the meanSum = 125, Count = 6, Mean = 125 ÷ 6 ≈ 20.8.
    3. 3Find the medianOrdered: 11, 12, 13, 14, 15, 60 → Median = (13 + 14) ÷ 2 = 13.5.
    4. 4Choose a measureThe student reports the mean (≈ 20.8) as the typical number of catches because it uses every game.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

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

Lesson 2.10Choose Appropriate Measures

ChallengeExtension

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 name of the correct group on each line.

    Sort by which measure is typically used in real life.

    Groups: Mean is typically reported Median is typically reported
    • Average temperature for the month
    • Average test score for a class (no outliers)
    • Median household income in a city
    • Median home price in a neighborhood
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Reasoning Error

    1. 1DataPlayer minutes per game: 32, 34, 30, 35, 33, 5
    2. 2Find meanSum = 169, Count = 6, Mean = 28.2
    3. 3Find medianOrdered: 5, 30, 32, 33, 34, 35 → Median = (32+33) ÷ 2 = 32.5
    4. 4ConclusionThe mean (28.2) is the best measure because it uses all the data.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A local newspaper reports that the average home price in a neighborhood is $450,000. The actual prices are: $180K, $200K, $190K, $210K, $195K, $1,725K. Is the reporter's claim misleading? Calculate the mean and median and explain which better represents a 'typical' home price.

    Write your answer

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