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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, smaller data set: 2, 5, 5, 8, 11. First, what is the median (the middle value)? The lower half is 2, 5 and the upper half is 8, 11. What is Q1? What is Q3? What are the lowest and highest values? Now picture the box stretching from Q1 to Q3 with the median line inside. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartThe values 4, 6, 9, 12 and 19 are already in order. What is the median?

   1. A9
   2. B10
   3. C6
   4. D12

   How do you know?
3. 3

   Warm restartOrder these values from least to greatest: 6, 13, 4, 9 and 3. What is the median?

   1. A6
   2. B7
   3. C4
   4. D13

   How do you know?
4. 4

   Warm restartFind the median of 4, 8, 6, 10.

   1. A7
   2. B6
   3. C8
   4. D28

   How do you know?

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 Team A's IQR?

   1. A16
   2. B35
   3. C60
   4. D10

   Why is that the answer?
2. 6

   Think it throughWhat is Team B's IQR?

   1. A10
   2. B45
   3. C61
   4. D16

   How do you know? Give a second reason as well.
3. 7

   Think it throughIs the fan right that Team B is better because of the 80-point game?

   1. ANo — one high game is a single extreme value, not typical performance
   2. BYes — 80 is the highest score in the data
   3. CNo — Team A's maximum is higher
   4. DYes — the maximum always decides

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelThe IQR is Q3 − Q1 = 26 − 10 = 16. What does this tell you about the middle 50% of scorers?

Use the words

Fill each blank with a word from the bank.

• A box plot shows the ___-number summary: least, Q1, median, Q3, greatest.
• A graph that shows data with a box and whiskers based on the five-number summary is a ___.
• The middle value of the data, shown as a line inside the box, is the ___.
• A value that divides the data into four equal parts is a ___.

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 Display Data: Box Plots is treating a quartile as just one data point instead of the median of a half — for the lower half 4, 8, 10, 14, some students pick 10 (the last value) as Q1 instead of finding the median of that half: Q1 = (8 + 10) ÷ 2 = 9.
2. 10

   Say moreAs you draw the box from Q1 to Q3, what does the length of the box tell you about the players' scores?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The table shows 25 sixth graders' times to finish a 5-kilometer road race.

   Show your work

Last check

These two come from Lesson 2.3. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A box plot has Q1 = 20 and Q3 = 36. What is the IQR and what does it represent?

   1. AIQR = 16; it is the spread of the middle 50% of the data
   2. BIQR = 56; it is the total of Q1 and Q3
   3. CIQR = 28; it is the median between Q1 and Q3
   4. DIQR = 36; it is the value of Q3

   Explain your choice.
2. 13

   From Lesson 2.3Explain your thinking — Data set: 4, 7, 10, 7, 12. What is the median, and what does it tell you?

   1. A7 — a typical value in this set is about 7
   2. B10 — it is the middle number as the list is written
   3. C8 — it is the average of all five values
   4. D12 — it is the largest value

   How do you know?
3. 14

   From Lesson 2.3What is the median of the 10 scores?

   1. A88
   2. B87
   3. C92
   4. D86.6

   How do you know?

Be honest — this tells your teacher what to do next