Describe Data by Mean Absolute Deviation

6.DS.6c · Unit 2 · Lesson 9

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 / TérminoDefinition / 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

  1. The mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?
    1. 4
    2. −4
    3. 26
    4. 11
  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.
  3. Match each MAD value to what it tells you about the data.
  4. Find the MAD Error
    1. Step 1: Data set — 5, 10, 15, 20, 25
    2. Step 2: Find mean — Sum = 75, Count = 5, Mean = 15
    3. Step 3: Find deviations — −10, −5, 0, 5, 10
    4. Step 4: Find MAD — MAD = (−10 + −5 + 0 + 5 + 10) ÷ 5 = 0

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: