Mean Absolute Deviation

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

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.

📖 See Learn It for the explanation and worked examples, and the Vocab tab for the words. These are your notes to fill in and keep.

✏️ Fill in each blank as we go. Use the Word Bank to help you.

📚 Word Bank — fill each blank with the best word

👆 Tap any word to see what it means and a picture.

Level 3: try the blanks from memory first, then check the bank.

1The average distance of each value from the mean is the .
2How far a single value is from the mean is its .
3The distance of a number from zero, always positive, is its .
4How far apart the data values are from each other is the .
5The way data values are spread out is the .
6How much the data values differ is the .

Write About the Math Guided ESOL writing

Use the support level you need. Every level answers the same math question.

1. Understand the Question

explain

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?

Your job: Answer the question. Use math evidence. Explain how the evidence proves your answer.Responde la pregunta. Usa evidencia matemática. Explica cómo la evidencia demuestra tu respuesta.

2. Plan Your Math Words

Check at least two words you will use.

Mean Absolute Deviation — The average distance of each number from the mean.Desviación media absoluta — La distancia promedio de cada número a la media. Deviation — How far a number is from the mean.Desviación — Qué tan lejos está un número de la media. Absolute Value — How far a number is from zero. It is always positive.Valor absoluto — Qué tan lejos está un número de cero. Siempre es positivo. Spread — How far apart the numbers are.Dispersión — Qué tan separados están los números. Data distribution — How the data looks: where it sits and how spread out it is.Distribución de datos — Cómo se ven los datos: dónde están y qué tan separados están.

Say it first: Say your idea to a partner or quietly to yourself before you write.Di tu idea a un compañero o en voz baja antes de escribir.

We use absolute value so the deviations are all ___.Usamos el valor absoluto para que las desviaciones sean todas ___.

3. Build Your Explanation

Model the parts: This model shows the parts of an explanation. It does not answer your writing question.

Claim: Two data sets can share a mean but differ in how spread out they are.

Evidence: Students choose Player A as more consistent and recognize that equal means hide different spreads.

Reasoning: This evidence connects the definition of mean absolute deviation to the mathematical claim.

Start

Most language support

Complete the frames. Use the word bank.Completa las oraciones. Usa el banco de palabras.

We use absolute value so the deviations are all ___.Usamos el valor absoluto para que las desviaciones sean todas ___.
Without absolute value, the deviations would add up to ___.Sin valor absoluto, las desviaciones sumarían ___.

Build

Some language support

Write two connected sentences. Use because, so, or but.Escribe dos oraciones conectadas. Usa porque, entonces o pero.

My claim is ___.Mi afirmación es ___.
I know because ___.Lo sé porque ___.
So ___.Entonces ___.

Explain

Light language support

Write a claim, give math evidence, and explain your reasoning.Escribe una afirmación, da evidencia matemática y explica tu razonamiento.

My claim is ___.Mi afirmación es ___.
My math evidence is ___.Mi evidencia matemática es ___.
This proves ___ because ___.Esto demuestra ___ porque ___.

4. Check Your Explanation

I answered the question.Respondí la pregunta. I used math evidence: numbers, an equation, a model, or a comparison.Usé evidencia matemática: números, una ecuación, un modelo o una comparación. I explained how the evidence proves my answer.Expliqué cómo la evidencia demuestra mi respuesta. I used at least two math words.Usé por lo menos dos palabras matemáticas. I reread complete sentences and punctuation.Volví a leer mis oraciones completas y la puntuación.