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

Lesson 2.9Comparing Sets with MAD

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.

Start hereWords for this lesson

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

Word	What it means	Example
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 72, value 78 → 6
Absolute ValueSpanish: Valor absoluto	How far a number is from zero. It is never negative.	\|−3\| = 3 and \|3\| = 3 — both are 3 units from zero
SpreadSpanish: Dispersión	How far apart the numbers are.	Low spread: 8, 9, 10, 11 (close together). High spread: 2, 9, 10, 25 (far apart)
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 examplecomparing two sets that share a mean

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

City A highs: 46, 50, 54, 58. City B highs: 36, 48, 56, 68. Each city has a mean of 52.

Measure every temperature's distance from the shared mean of 52.
City A distances: 6, 2, 2, 6. City B distances: 16, 4, 4, 16.
Average each list of distances on its own to get that city's MAD.
A larger MAD means the values sit further away from the mean.

Answer: City A has a MAD of 4 and City B a MAD of 10, so City B's highs vary far more.

Now you trySame steps, your turn

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

Team P scores: 15, 19, 23, 27. Team Q scores: 11, 17, 25, 31. Each team has a mean of 21.

Distances from the mean for Team P:
Distances from the mean for Team Q:
MAD of Team P: MAD of Team Q:
More consistent team: How do you know?

Answer:both MADs and the more consistent team

Say it and write itSentence starters

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

Both sets have a mean of .
The MAD of is and the MAD of is .
is more consistent because .
A larger MAD means the values .

Word bank mean absolute deviationdeviationdistancemeanspreadvariationconsistentcomparelargersmallertypicalcenter

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 nonnegative distance, including zero: |−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 2.9Comparing Sets with MAD

Apply Day · Version ASupported 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.

1Complete each step, then write the final answer.

Find the MAD of this data set: 1, 4, 7.
Show your work
Hint The mean is 4. Find how far 1, 4 and 7 are from 4.
Final answer:
2Complete each step, then write the final answer.

Find the MAD of this data set: 5, 6, 10, 11.
Show your work
Hint The values add to 32. Find the mean, then each distance from it.
Final answer:
3Complete each step, then write the final answer.

Find the MAD of this data set: 2, 4, 4, 6.
Show your work
Hint The mean is 4. Two values are 0 away from it.
Final answer:

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.6c

Lesson 2.9Comparing Sets with MAD

Apply Day · Version BCore 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.

1Circle 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
Show your work
2Complete 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:
3Complete each step, then write the final answer.

Find the MAD of this data set: 3, 7, 8, 10.
Show your work
Final answer:

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.6c

Lesson 2.9Comparing Sets with MAD

Apply Day · ChallengeExtension

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.

1Circle the letter of the best answer. Show how you know.
A data set is 3, 5, 9, 11 with a mean of 7. What is the mean absolute deviation?
1. A2
2. B3
3. C7
4. D28
Put the data in order

Work
2Complete 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:
3Complete each step, then write the final answer.

Find the MAD of this data set: 5, 7, 8, 10, 15.
Show your work
Final answer:

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