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

Lesson 2.92.9 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the mean absolute deviation (MAD) to describe how spread out data is, explain how I can tell, and judge a case I have not seen before.

Why This Matters This is your challenge small group for Lesson 2.9. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

Start hereWords for this lesson

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

WordWhat it meansExample
Mean Absolute DeviationSpanish: Desviación media absoluta The average distance of data values from the mean; it describes spread. Written as MAD
DeviationSpanish: Desviación How far a number is from the mean. Mean 19, value 23 → 4
Absolute ValueSpanish: Valor absoluto How far a number is from zero. It is never negative. Distance is never below zero
SpreadSpanish: Dispersión How far apart the numbers are. Small MAD = tight set
Data distributionSpanish: Distribución de datos How the data looks: where it sits and how spread out it is. A set clustered tightly around the mean has low MAD; a set spread far from the mean has high MAD
VariabilitySpanish: Variabilidad How spread out the numbers are. Low variability (MAD = 1): very consistent. High variability (MAD = 8): very spread out

How it worksWorked example

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

Four plants grew 3, 7, 8 and 10 cm. Find the MAD.

  1. Mean: 28 ÷ 4 = 7.
  2. Distances from 7: 4, 0, 1, 3.
  3. Sum = 8, and 8 ÷ 4 = 2.

Answer: MAD = 2 cm

Now you trySame steps, your turn

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

Find the MAD of this data set: 9, 10, 11.

Answer:

Say it and write itSentence starters

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

  • The mean of this set is .
  • The distance from to the mean is .
  • The distances total , and there are values.
  • The MAD is , which means .

Word bank mean absolute deviationdeviationdistanceabsolute valuemeanspreadaveragetotaldividetypicalconsistentvariation

Watch out!A common mistake

A common mistake in Mean Absolute Deviation is adding the signed deviations (value − mean) instead of their absolute values, so the positives and negatives cancel out to 0. For 6, 8, 10, 12 (mean = 9), the deviations are −3, −1, 1, 3

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

Lesson 2.92.9 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can find the mean absolute deviation (MAD) to describe how spread out data is, explain how I can tell, and judge a case I have not seen before.

Why This Matters This is your challenge small group for Lesson 2.9. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  1. 1Complete each step, then write the final answer.
    Team ADistance from 10Team BDistance from 10
    4691
    91111
    100100
    13382
    144122
    Team A's scores are farther from the mean.

    Team A scored 4, 9, 10, 13 and 14 goals. Team B scored 9, 11, 10, 8 and 12 goals. Both means are 10. Which team is more consistent?

    1. 1Find each distance from 10 for Team A.
    2. 2What is Team A's MAD?
    3. 3What is Team B's MAD?
    4. 4Which team is more consistent?
    Final answer:
  2. 2Complete each step, then write the final answer.
    2345678910111213
    One value is far from the others.

    Find the MAD of 3, 4, 5, 6, 12. The MAD of 3, 4, 5, 6 alone is 1. Why does 12 change it so much?

    1. 1The values add to 30. What is the mean?
    2. 2Find each distance from 6. Then find the MAD.
    3. 3Why does the value 12 make the MAD larger?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the MAD of this data set: 1.5, 2.5, 3.5, 4.5.

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

    Five snacks cost $2, $5, $3, $6 and $4. Find the MAD of the prices.

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

    Slide heights at a water park are 60, 75, 80, 85 and 100 feet. Find the MAD of the heights.

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

    Kai finds the deviations of 2, 6, 7, 9 from their mean, 6. He gets −4, 0, 1 and 3. He adds them and says the MAD is 0. What is the MAD?

    Show your work
    Final answer:

Explain your thinkingTwo classes have the same mean test score. One class has a MAD of 3. The other has a MAD of 12. Which class has scores more alike? Defend it.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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