Describe Data by Mean Absolute Deviation
I can find the mean absolute deviation (MAD) to describe how spread out data is.
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🎯 Content Objective / Objetivo de contenido
I can find the mean absolute deviation (MAD) to describe how spread out data is.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
The forecast shows seven high temperatures and their mean is 79°F. Which day is farthest from the mean, and what does that tell you about the week?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
High Temperature
The forecast shows the expected high temperatures for a week. The mean high temperature for the week is 79°F. How can you describe the variation in high temperatures over the week?
Concept Launch
💡 What is the mean absolute deviation (MAD)?
The mean absolute deviation, or MAD, is the average distance of each value from the mean. It tells you how spread out the data is: a small MAD means the data is close together, and a large MAD means it is spread out.
Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count). 1. Calculate the mean of the data set. 2. Find the distance (absolute difference |value − mean|) for each data point. 3. Average the distances: Add all distances and divide by the count
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Mean Absolute Deviation Desviación media absoluta |
The average distance of data values from the mean; it describes spread. La distancia promedio de los valores de datos respecto a la media; describe la dispersión. |
MAD = sum of absolute distances from the mean ÷ number of values. | |
| Deviation Desviación |
How far a number is from the mean. Qué tan lejos está un número de la media. |
If mean = 20 and value = 17, deviation = 17 − 20 = −3 (3 below the mean) | |
| Absolute Value Valor absoluto |
How far a number is from zero. It is never negative. Qué tan lejos está un número de cero. Nunca es negativo. |
|−3| = 3 and |3| = 3 — both are 3 units from zero | |
| Spread Dispersión |
How far apart the numbers are. Qué tan separados están los números. |
Low spread: 8, 9, 10, 11 (close together). High spread: 2, 9, 10, 25 (far apart) | |
| Data distribution Distribución de datos |
How the data looks: where it sits and how spread out it is. Cómo se ven los datos: dónde están y qué tan separados están. |
A set clustered tightly around the mean has low MAD; a set spread far from the mean has high MAD | |
| Variability Variabilidad |
How spread out the numbers are. Qué tan separados están los números. |
Low variability (MAD = 1): very consistent. High variability (MAD = 8): very spread out |
Which Word Fits?
The average distance of each value from the mean is the ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
The forecast shows seven high temperatures and their mean is 79°F. Which day is farthest from the mean, and what does that tell you about the week?
👂 Listen For
Students choose Player A as more consistent and recognize that equal means hide different spreads.
Extend: Predict: which player will have the larger MAD, and what does a larger MAD say about consistency?
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Calculate the Mean Absolute Deviation (MAD) for Player A's scores: 18, 22, 20, 24, 16. Follow each step.
✍️ Explore Discourse
Player A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
To find the MAD for Player A (18, 22, 20, 24, 16, mean 20), why do we take the ABSOLUTE VALUE of each deviation before averaging?
👂 Listen For
A strong answer explains deviations above and below the mean would cancel to zero, so absolute value keeps each as a positive distance.
Extend: Compute and justify: find the MAD of 18, 22, 20, 24, 16. Show the deviations, take absolute values, and average them.
Practice Check A
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?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Statistical vs Not Sort
Drag each question into the correct column.
✍️ Justify Your Thinking
Sort these data sets from LEAST spread out (lowest MAD) to MOST spread out (highest MAD).
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count). 1. Calculate the mean of the data set. 2. Find the distance (absolute difference |value − mean|) for each data point. 3. Average the distances: Add all distances and divide by the count" — and it works because ___.
Because Mean Absolute Deviation means ___, but a tricky part is ___, so I have to ___.
A common mistake with Mean Absolute Deviation is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Deviation to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count). 1. Calculate the mean of the data set. 2. Find the distance (absolute difference |value − mean|) for each data point. 3. Average the distances: Add all distances and divide by the count because ___
Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count). 1. Calculate the mean of the data set. 2. Find the distance (absolute difference |value − mean|) for each data point. 3. Average the distances: Add all distances and divide by the count but ___
Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count). 1. Calculate the mean of the data set. 2. Find the distance (absolute difference |value − mean|) for each data point. 3. Average the distances: Add all distances and divide by the count so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Fill in the table using today's strategy.
| Score | Deviation (Score − Mean) | Absolute Deviation |
|---|---|---|
| 18 | ||
| 22 | ||
| 20 | ||
| 24 | ||
| 16 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
Two soccer goalkeepers track goals allowed per game over 6 games. Keeper A: 1, 2, 1, 3, 2, 1 (mean = 1.67, MAD ≈ 0.67). Keeper B: 0, 4, 1, 3, 0, 2 (mean = 1.67, MAD ≈ 1.33). The coach needs to pick a starter for the championship game.
✍️ Connection Reasoning
Both keepers allow the same average goals. Which should the coach pick and why?
Both keepers have a mean of ___. Keeper A's MAD is ___, which means ___. Keeper B's MAD is ___, which means ___. The coach should pick ___ because ___.
Turn & Talk — Connect
Two keepers both allow a mean of 1.67 goals, but Keeper A's MAD is 0.67 and Keeper B's is 1.33. Which keeper should the coach start in the championship, and why?
👂 Listen For
Students pick Keeper A and explain a smaller MAD (0.67) means goals allowed stay close to the mean, so performance is more reliable.
Extend: Critique: when might a coach actually prefer the LESS consistent keeper (higher MAD)? Defend with a scenario.
Summarize: Describe Data by Mean Absolute Deviation
Mean Absolute Deviation (MAD). Formula: MAD = (Sum of distances from mean) ÷ (Total count). 1. Calculate the mean of the data set. 2. Find the distance (absolute difference |value − mean|) for each data point. 3. Average the distances: Add all distances and divide by the count
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Data set: 4, 8, 6, 10, 2. The mean is 6. What is the MAD?
Bonus Exit Check
A data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students choose Player A as more consistent and recognize that equal means hide different spreads.
• A strong answer explains deviations above and below the mean would cancel to zero, so absolute value keeps each as a positive distance.
• Students pick Keeper A and explain a smaller MAD (0.67) means goals allowed stay close to the mean, so performance is more reliable.
• Students compute absolute deviations 2, 2, 0, 4, 4 (sum 12), divide by 5, and report MAD = 2.4.
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.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 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.
✓ Practice 2: 4 — Deviation = 11 − 15 = −4. Absolute deviation = |−4| = 4.
✓ Practice 3: 3 — Sum of absolute deviations = 3 + 1 + 5 + 2 + 4 = 15. MAD = 15 ÷ 5 = 3.
✓ Practice 4: 6 — Deviation = 26 − 20 = 6. Absolute deviation = |6| = 6.
✓ Exit ticket: 2.4 — Deviations: −2, 2, 0, 4, −4. Absolute deviations: 2, 2, 0, 4, 4. Sum = 12. MAD = 12 ÷ 5 = 2.4.