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

Lesson 2.92.9 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the mean absolute deviation (MAD) to describe how spread out data is — 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
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 examplefinding the mean absolute deviation

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

Five snack prices in cents are 80, 90, 100, 110, 120. Find the mean absolute deviation.

  1. Find the mean: the five prices total 500, and sharing that evenly gives 100.
  2. Measure each price's distance from 100: 20, 10, 0, 10, 20.
  3. Add the distances. They come to 60.
  4. Share that total distance among the five prices.

Answer: The MAD is 12 cents — a typical price sits about 12 cents away from the mean.

Now you trySame steps, your turn

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

Five backpack weights in ounces are 33, 36, 37, 38, 41. Find the MAD.

  1. Add the five weights: Mean:
  2. Distance of each weight from the mean: , , , ,
  3. Total of the distances:
  4. Share that total among the number of values. MAD: ounces
Answer:mean absolute deviation in ounces

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 outA 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 — they sum to 0, but that is NOT the MAD. Before averaging, take the absolute value of every deviation so each becomes a positive distance: |−3| = 3, |−1| = 1, |1| = 1, |3| = 3. Sum = 8, so MAD = 8 ÷ 4 = 2. A MAD of exactly 0 is a warning sign — it only happens if every value in the data set equals the mean.

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

Lesson 2.92.9 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 find the mean absolute deviation (MAD) to describe how spread out data is — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    123456789
    Find the mean. Then count how far each value is from it.

    Find the mean absolute deviation (MAD) of this data set: 2, 3, 5, 7, 8.

    1. 1Add the values and divide by 5. What is the mean?
    2. 2How far is each value from 5?
    3. 3Add the distances and divide by 5. What is the MAD?
    Final answer:
  2. 2Complete each step, then write the final answer.
    012345678910
    This time the MAD is not a whole number.

    Find the MAD of this data set: 1, 4, 6, 9.

    1. 1Find the mean.
    2. 2How far is each value from 5?
    3. 3Add the distances. What is the total?
    4. 4Divide the total by 4. What is the MAD?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the MAD of this data set: 2, 5, 8.

    Show your work

    Hint First find the mean. Then find how far each value is from it.

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

    A player scored 12, 18, 15, 20 and 10 points in 5 games. Find the MAD of the scores.

    Show your work

    Hint The scores add to 75. Find the mean, then each distance from it.

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

    The high temperatures for 4 days were 60, 64, 70 and 66 degrees. Find the MAD of the temperatures.

    Show your work

    Hint The four temperatures add to 260. Find the mean first.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.

    Set A is 5, 6, 7. Set B is 1, 6, 11. Both sets have a mean of 6. Which set has the greater MAD?

    1. ASet A
    2. BSet B
    3. CThey have the same MAD

    Hint Find how far each value is from 6 in both sets.

    Show your work

Explain your thinkingSet B has the greater MAD. What does a greater MAD tell you about the data? Use the number line to explain.

Sentence starter A greater MAD means the values are ___ from the mean. · Set ___ is more spread out because ___.

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