6.DS.6c Group 2 · Challenge

Practice Set · Part 1

Describe Data by Mean Absolute Deviation

Pick up where we left off

Name: Date: Group:

Where we left off

Our goal: I can find the mean absolute deviation (MAD) to describe how spread out data is, explain how I can tell, and judge a case I have not seen before.

The big idea: MAD = the average of how far each number is from the mean (always a positive distance) — and you can say why it is true, and where it would stop being true.

Model to copy — Watch me

  1. My data set: 6, 8, 10, 12. First I find the mean: 6 + 8 + 10 + 12 = 36, then 36 ÷ 4 = 9. The mean is 9.
  2. Next I find each deviation (value − mean): 6−9 = −3, 8−9 = −1, 10−9 = 1, 12−9 = 3.
  3. Then I take the absolute value of each (the distance, always positive): 3, 1, 1, 3.
  4. Finally I average those distances: 3 + 1 + 1 + 3 = 8, then 8 ÷ 4 = 2. So the MAD = 2 points.

Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

  1. 1

    Same stepsFinish what the group started. Use the model above, step for step.

    Try it together — then prove it: New data set: 9, 10, 11. First, what is the mean? Add the three numbers and divide by 3. Now find how far each number is from the mean. What is the distance for 9? For 10? For 11? Add those distances and divide by 3. Is this MAD small or large? What does that tell us about the spread? Now prove it: say why that move had to work at all — not just that it did.
    Show your work
  2. 2

    Warm restartFind the mean of 10, 14, 8, 12 and 16.

    1. A12
    2. B14
    3. C10
    4. D60

    How do you know?

  3. 3

    Warm restartFour friends have 6, 9, 4 and 5 stickers. If they share them equally, how many does each get?

    1. A6
    2. B24
    3. C5
    4. D4

    How do you know?

  4. 4

    Warm restartA student's first three quiz scores are 82, 90 and 86. What score on a fourth quiz gives a mean of 87?

    1. A90
    2. B88
    3. C86
    4. D92

    How do you know?

2.9 Small Group · Group 2 · Practice SetPart 1 of 4
6.DS.6c Group 2 · Challenge

Practice Set · Part 2

Describe Data by Mean Absolute Deviation

Keep going

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

  1. 5

    Think it throughWhat is each keeper's mean goals allowed per game?

    1. Aabout 1.67
    2. B10
    3. C6
    4. D2

    Why is that the answer?

  2. 6

    Think it throughWhat does a smaller MAD tell you?

    1. AThe values stay closer to the mean — the keeper is more consistent
    2. BThe keeper allowed fewer goals overall
    3. CThe keeper played fewer games
    4. DThe mean is wrong

    How do you know? Give a second reason as well.

  3. 7

    Think it throughWhich keeper should the coach start, and why?

    1. AKeeper A, because the smaller MAD (0.67) means more consistent performance
    2. BKeeper B, because two shutouts is best
    3. CEither one, because the means are equal
    4. DKeeper B, because a larger MAD means more skill

    Explain your thinking. What would have to change for a different choice to be right?

  4. 8

    Back to the modelPlayer A's MAD is 2.4 points. If Player B's MAD is 7.2 points, what does that tell you about their consistency?

2.9 Small Group · Group 2 · Practice SetPart 2 of 4
6.DS.6c Group 2 · Challenge

Practice Set · Part 3

Describe Data by Mean Absolute Deviation

Words and reasoning

Word bank · Banco de palabras

Mean Absolute Deviation (Desviación media absoluta)Deviation (Desviación)Absolute Value (Valor absoluto)Spread (Dispersión)Data distribution (Distribución de datos)Variability (Variabilidad)

Use the words

Fill each blank with a word from the bank.

Explain the thinking

  1. 9

    Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

    The 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.
  2. 10

    Say moreTo 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?

  3. 11

    Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The forecast shows the expected high temperature for each day of this week: 75, 77, 78, 79, 80, 82 and 82 degrees Fahrenheit. The mean high for the week is 79 degrees, marked by the dashed line.

    Show your work
2.9 Small Group · Group 2 · Practice SetPart 3 of 4
6.DS.6c Group 2 · Challenge

Practice Set · Part 4

Describe Data by Mean Absolute Deviation

Show what you know

Last check

These two come from Lesson 2.8. If they are shaky, that is the lesson to revisit — not this one.

  1. 12

    Show what you knowExplain your thinking — Data set: 4, 8, 6, 10, 2. The mean is 6. What is the MAD?

    1. A2.4
    2. B6
    3. C0
    4. D12

    Explain your choice.

  2. 13

    From Lesson 2.8Explain your thinking — Data set: 8, 12, 10, 14. What is the mean?

    1. A11
    2. B44
    3. C12
    4. D10

    How do you know?

  3. 14

    From Lesson 2.8Her nine games total 13 points below the target mean and 11 points above it. What must game 10 be for the data to balance at 15?

    1. A17 points — 2 above the target mean
    2. B13 points — 2 below the target mean
    3. C15 points — exactly the target mean
    4. D24 points — enough to double the points above

    How do you know?

Be honest — this tells your teacher what to do next

I can…Not yetGetting thereGot it
I can find the mean absolute deviation (MAD) to describe how spread out data is, explain how I can tell, and judge a case I have not seen before.
I can explain why it works: MAD = the average of how far each number is from the mean (always a positive distance)…
I can justify my answer to a skeptic and connect it to a second strategy or representation.

One question I want to ask my group next time