Describe Data by Mean Absolute Deviation
Name Period
Objectives / Objetivos
Content Objective: I can find the mean absolute deviation (MAD) to describe how spread out data is.
Language Objective: I can explain my work using the words mean absolute deviation, deviation, absolute value, and spread.
Key Idea / Idea clave
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
I Notice / Observo
- Both players have the same mean. Looking at the listed scores, what is different about them?
- Using the dot plot of Player A's scores and the scores listed for Player B in the story, which player's scores stay closer to 20?
I Wonder / Me pregunto
- How can we measure how spread out each player's scores are?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| 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. |
| Deviation Desviación | How far a number is from the mean. Qué tan lejos está un número de la media. |
| 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. |
| Spread Dispersión | How far apart the numbers are. Qué tan separados están los números. |
| 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. |
| Variability Variabilidad | How spread out the numbers are. Qué tan separados están los números. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?
- A 4
- B −4
- C 11
- D 26
Answer:
2. Deviation Detective: the quiz scores are 12, 8, 10, 14, 6 and the mean is 10. Complete each deviation and absolute deviation, then compute the MAD.
Complete each empty cell. Show your reasoning below.
| Score | Deviation (Score − Mean) | Absolute Deviation |
|---|---|---|
| 12 | ||
| 8 | ||
| 10 | ||
| 14 | ||
| 6 |
3. Match each MAD value to what it tells you about the data.
Write the letter of the matching item in the blank.
| 1. | MAD = 1.5 | A. | Very spread out data | |
| 2. | MAD = 8.0 | B. | Very consistent data | |
| 3. | MAD = 0 | C. | All values are identical | |
| 4. | MAD = 4.2 | D. | Moderate spread |
4. Find the MAD Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: