Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. Find the MAD of this data set: 9, 10, 11.
   2. Find the mean. (30 ÷ 3 = 10)
   3. Find each distance from 10. Then find the MAD. (Distances 1, 0, 1 → (1 + 0 + 1) ÷ 3 = 2/3)
   4. The deviations −1, 0 and 1 add to 0. Why do we use distances instead? (Signed deviations always add to 0. Then every data set would look like it has no spread.)

   Show your work
2. 2

   Quick reviewFind the mean of 10, 14, 8, 12 and 16. 🔊 Listen 💡 Hint

   1. A10
   2. B12
   3. C14
   4. D60

   How do you know?
3. 3

   Quick reviewFour friends have 6, 9, 4 and 5 stickers. If they share them equally, how many does each get? 🔊 Listen 💡 Hint

   1. A4
   2. B5
   3. C6
   4. D24

   How do you know?
4. 4

   Quick reviewA student's first three quiz scores are 82, 90 and 86. What score on a fourth quiz gives a mean of 87? 🔊 Listen 💡 Hint

   1. A86
   2. B88
   3. C90
   4. D92

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhat is each keeper's mean goals allowed per game? 🔊 Listen 💡 Hint

   1. Aabout 1.67
   2. B2
   3. C6
   4. D10

   Why is that the answer?
2. 6

   Think it throughWhat does a smaller MAD tell you? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   1. AKeeper B, because two shutouts is best
   2. BEither one, because the means are equal
   3. CKeeper A, because the smaller MAD (0.67) means more consistent performance
   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? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• The average distance of each value from the mean is the ___.
• How far a single value is from the mean is its ___.
• The distance of a number from zero, never negative (zero is allowed), is its ___.
• How far apart the data values are from each other is the ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint
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. 🔊 Listen 💡 Hint

   Show your work

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? 🔊 Listen 💡 Hint

   1. A0
   2. B2.4
   3. C6
   4. D12

   Explain your choice.
2. 13

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

   1. A10
   2. B11
   3. C12
   4. D44

   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? 🔊 Listen 💡 Hint

   1. A13 points — 2 below the target mean
   2. B15 points — exactly the target mean
   3. C17 points — 2 above the target mean
   4. D24 points — enough to double the points above

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.