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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: Class A's box plot reads: least 62, Q1 74, median 81, Q3 87, greatest 90. Find the range first. Range = 90 − 62 = 28 points from the lowest score to the highest. Now the IQR: subtract Q1 from Q3. IQR = 87 − 74 = 13 points across the middle half. Say what each one means: the whole class's scores span 28 points, but the middle half of the class is packed into 13 points. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA box plot has minimum 4, Q1 = 7, median = 10, Q3 = 14 and maximum 20. Which value splits the data in half?

   1. A10
   2. B7
   3. C14
   4. D12

   How do you know?
3. 3

   Warm restartIn that same box plot, what does the LEFT edge of the box show?

   1. AQ1, which is 7
   2. BThe minimum, which is 4
   3. CThe median, which is 10
   4. DQ3, which is 14

   How do you know?
4. 4

   Warm restartFind the five-number summary of 2, 5, 6, 8, 9, 11, 14.

   1. A2, 5, 8, 11, 14
   2. B2, 6, 8, 9, 14
   3. C2, 5, 6, 11, 14
   4. D2, 8, 11, 14, 14

   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 the range of Class A's scores?

   1. A28 points
   2. B13 points
   3. C81 points
   4. D90 points

   Why is that the answer?
2. 6

   Think it throughWhat is the interquartile range of Class B's scores?

   1. A8 points
   2. B20 points
   3. C14 points
   4. D81 points

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

   Think it throughBoth classes have a median of 81. What do the smaller range and smaller IQR tell you about Class B?

   1. AClass B's scores are less spread out, so more students scored near the median
   2. BClass B's best score was higher
   3. CClass B had fewer students
   4. DClass B's median is actually larger

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

   Back to the modelBoth numbers describe spread. Why might a coach trust the IQR more than the range when one player had a record-breaking night?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• 94 − 68 = 26
• 88 − 75.5 = 12.5
• Uses the greatest and least values
• Uses the third quartile and the first quartile
• Describes the middle half of the data
• Describes every value in the data set
• The width of the box on a box plot
• One unusually high value stretches it a lot

Use the words

Fill each blank with a word from the bank.

• The range uses the ___ values; the interquartile range uses the ___.
• Subtract the least value from the ___ value to find the range.
• Numbers that split ordered data into four equal parts are ___.
• The spread of the middle half of the data, Q3 − Q1, is the ___ ___.

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 with Range and Interquartile Range is adding the two quartiles instead of subtracting them — writing IQR = Q3 + Q1.
2. 10

   Say moreWhy does the range change a lot when one unusual value is added, but the IQR barely moves?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The team's data analyst pulls up two dot plots. Fan ages at last night's game: 18, 19, 20, 20, 21, 21, 22, 68 (one grandparent came too). Roster shoe sizes: 9, 10, 10, 10.5, 11, 11, 11.5.

   Show your work

Last check

These two come from Lesson 2.4. 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, with a least value of 10 and a greatest value of 50. What is the IQR, and what does it tell you?

   1. AIQR = 16; the middle half of the data spans 16 units
   2. BIQR = 40; the data spans 40 units from end to end
   3. CIQR = 56; the quartiles add to 56
   4. DIQR = 28; 28 is halfway between the quartiles

   Explain your choice.
2. 13

   From Lesson 2.4Explain 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

   How do you know?
3. 14

   From Lesson 2.4Is 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

   How do you know?

Be honest — this tells your teacher what to do next