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.

   Let's try together: Data set A: 4, 5, 6, 7, 8. Are there any outliers? If not, which measure should we use, mean or median? Data set B: 4, 5, 6, 7, 40. Which value is an outlier here? For data set B, would the outlier pull the mean up or down? So which measure best shows a typical value?

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restartThe mean of a data set is 20. A value is 26. What is the absolute deviation?

   1. A−6
   2. B6
   3. C46
   4. D26
3. 3

   Warm restartThe mean of a data set is 15. One value is 11. What is the absolute deviation of that value from the mean?

   1. A−4
   2. B26
   3. C4
   4. D11
4. 4

   Warm restartA data set has absolute deviations of 3, 1, 5, 2, 4. What is the MAD?

   1. A5
   2. B3
   3. C15
   4. D1

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 the mean ticket price?

   1. A$85
   2. B$51
   3. C$260
   4. D$50

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughWhat is the median ticket price?

   1. A$51
   2. B$85
   3. C$52
   4. D$50

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughWhich measure better describes a 'typical' ticket?

   1. AThe median, because the $260 outlier pulls the mean far above most prices
   2. BThe mean, because it uses every value
   3. CNeither — you should use the mode
   4. DThe mean, because $85 is between the extremes

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelWhat pattern do you notice about when median is the better choice?

   The median is better when the data has ___ because the mean gets pulled toward ___. The mean is better when the data is ___ because ___.

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• Basketball: Points per game — 18, 20, 19, 22, 21, 20 (no outliers, symmetric)
• Baseball: Home runs — 2, 3, 1, 2, 3, 2, 25 (one player hit 25)
• Soccer: Goals per season — 8, 10, 9, 11, 7, 10, 9 (clustered together)
• Football: Rushing yards — 45, 52, 48, 50, 210 (one breakout game)
• Swimming: 100m times — 58s, 59s, 57s, 60s, 58s (consistent data)
• Track: Long jump — 12ft, 13ft, 11ft, 14ft, 42ft (one record jump)

Use the words

Fill each blank with a word from the bank.

• A center chosen because it describes the data fairly is an ___ ___ ___ ___.
• The average of a data set is the ___.
• The middle value when data is in order, often best when there is an outlier, is the ___.
• A value far from the rest of the data, which can pull the mean, is an ___.

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 Appropriate Measures is defaulting to the mean just because "it uses all the data," without first checking whether an outlier or skewed shape is present.
2. 10

   Say moreAs you sort scenarios into 'Use Mean' or 'Use Median,' what clue tells you a data set needs the median instead of the mean?

   I use the median when the data has ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   Show your work

Last check

These two come from Lesson 2.9. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: Data set: 15, 18, 16, 17, 15, 72. Which measure of center best represents the data?

   1. AMedian, because 72 is an outlier
   2. BMean, because it uses all values
   3. CMean, because it is always best
   4. DNeither works for this data

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 2.9Quick check — you've got this: Data set: 4, 8, 6, 10, 2. The mean is 6. What is the MAD?

   1. A2.4
   2. B6
   3. C0
   4. D12
3. 14

   From Lesson 2.9Which 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

Be honest — this tells your teacher what to do next