Unit 8 · Standard 6.SP.5c
Mean Absolute Deviation
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Data: 8, 10, 12. Mean = 10. Distances from mean: 2, 0, 2. MAD = (2+0+2) ÷ 3 = 1.33
Mean Absolute Deviation
The average distance of each number from the mean.
If mean = 20 and value = 17, deviation = 17 − 20 = −3 (3 below the mean)
Deviation
How far a number is from the mean.
|−3| = 3 and |3| = 3 — both are 3 units from zero
Absolute Value
How far a number is from zero. It is always positive.
Low spread: 8, 9, 10, 11 (close together). High spread: 2, 9, 10, 25 (far apart)
Spread
How far apart the numbers are.
A set clustered tightly around the mean has low MAD; a set spread far from the mean has high MAD
Data distribution
How the data looks: where it sits and how spread out it is.
Low variability (MAD = 1): very consistent. High variability (MAD = 8): very spread out
Variability
How spread out the numbers are.
Key Ideas & Notes
- Coach wants to know which basketball player is more consistent: Player A scored 18, 22, 20, 24, 16 points in the last 5 games.
- Player B scored 10, 30, 25, 12, 23 points.
- Both players average 20 points per game.
- Which player would you count on to score close to 20 every night?
Think About It
- Both players have the same mean. What is different about their scores?
- Which player's scores stay closer to 20?
- Which player has the biggest single-game difference from 20?
My Notes
Guided Examples
Example 1
The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?
Solution: Deviation = 11 − 15 = −4. Absolute deviation = |−4| = 4.
Answer: A. 4
Example 2
A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?
Solution: Sum of absolute deviations = 3 + 1 + 5 + 2 + 4 = 15. MAD = 15 ÷ 5 = 3.
Answer: A. 3
Example 3
The mean of a data set is 20. A value is 26. What is the absolute deviation?
Solution: Deviation = 26 − 20 = 6. Absolute deviation = |6| = 6.
Answer: A. 6
Write About the Math The Writing Revolution
I can explain my work using the words mean absolute deviation, deviation, absolute value, and spread.
1. Kernel Sentence subject + verb
Model: Mean Absolute Deviation is the average distance of each number from the mean.Desviación media absoluta es la distancia promedio de cada número a la media.
Write a kernel sentence about mean absolute deviation. Use a subject and a verb.Escribe una oración base sobre desviación media absoluta. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Mean Absolute Deviation matters in mathDesviación media absoluta importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Mean Absolute Deviation matters in math because ___.Desviación media absoluta importa en matemáticas porque ___.
Mean Absolute Deviation matters in math, but ___.Desviación media absoluta importa en matemáticas, pero ___.
Mean Absolute Deviation matters in math, so ___.Desviación media absoluta importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about mean absolute deviation.Di un hecho verdadero sobre mean absolute deviation.
Mean absolute deviation ___.
Ask a question about mean absolute deviation.Haz una pregunta sobre mean absolute deviation.
How does ___ ?¿Cómo ___ ?
Show excitement about mean absolute deviation.Muestra entusiasmo sobre mean absolute deviation.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with mean absolute deviation.Dile a un compañero qué hacer con mean absolute deviation.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The MAD shows ___.La DMA muestra ___.
The data is spread out because ___.Los datos están dispersos porque ___.
This matters when ___.Esto importa cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Team A has MAD = 2.1 points. Team B has MAD = 6.8 points. Which team is more consistent?
- Team A — lower MAD means scores are closer to the mean
- Team B — higher MAD means better performance
- Both are equally consistent
- Cannot tell from MAD alone
2. Two runners have the same average time of 60 seconds. Runner A's MAD is 1.2 seconds. Runner B's MAD is 5.8 seconds. Which runner is the coach more likely to pick for a relay race that needs a reliable time?
- Runner A — lower MAD means more consistent times
- Runner B — higher MAD means faster potential
- Either — they have the same average
- Neither — MAD doesn't matter for relay races
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Two basketball teams both average 75 points per game. Team A's last 5 scores: 73, 76, 74, 77, 75. Team B's last 5 scores: 60, 90, 65, 85, 75. Calculate the MAD for each team and explain which team a coach would prefer if they need predictable scoring.
Sentence starter: Team A's MAD = ___. Team B's MAD = ___. Team A is ___ because ___. A coach would prefer Team ___ for predictable scoring because ___.
Reflect — Exit Ticket
Data set: 4, 8, 6, 10, 2. The mean is 6. What is the MAD?
- 2.4
- 6
- 0
- 12
Answer Key & Teacher Guide
- Try It 1: A. Team A — lower MAD means scores are closer to the mean — Lower MAD means less spread — Team A's scores stay closer to their average, making them more consistent.
- Try It 2: A. Runner A — lower MAD means more consistent times — Runner A's MAD of 1.2 means times are usually within 1.2 seconds of 60. Runner B's times vary more widely. For reliability, pick Runner A.
- Exit Ticket: A. 2.4 — Deviations: −2, 2, 0, 4, −4. Absolute deviations: 2, 2, 0, 4, 4. Sum = 12. MAD = 12 ÷ 5 = 2.4.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Mean Absolute Deviation is the average distance of each number from the mean.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).