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. Class A's box plot shows: least 62, Q1 74, median 81, Q3 87, greatest 90. Find the range and the IQR.
   2. Find the range. (90 − 62 = 28)
   3. Find the IQR. (87 − 74 = 13)
   4. Why is the IQR smaller than the range? (The IQR uses only the middle half of the data. The range uses all of it, from least to greatest.)

   Show your work
2. 2

   Quick reviewA box plot has minimum 4, Q1 = 7, median = 10, Q3 = 14 and maximum 20. Which value splits the data in half? 🔊 Listen 💡 Hint

   1. A7
   2. B10
   3. C12
   4. D14

   How do you know?
3. 3

   Quick reviewIn that same box plot, what does the LEFT edge of the box show? 🔊 Listen 💡 Hint

   1. AQ1, which is 7
   2. BQ3, which is 14
   3. CThe minimum, which is 4
   4. DThe median, which is 10

   How do you know?
4. 4

   Quick reviewFind the five-number summary of 2, 5, 6, 8, 9, 11, 14. 🔊 Listen 💡 Hint

   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?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhat is the range of Class A's scores? 🔊 Listen 💡 Hint

   1. A13 points
   2. B28 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? 🔊 Listen 💡 Hint

   1. A8 points
   2. B14 points
   3. C20 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? 🔊 Listen 💡 Hint

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

   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? 🔊 Listen 💡 Hint

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

   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? 🔊 Listen 💡 Hint
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. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

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

   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? 🔊 Listen 💡 Hint

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

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

   How do you know?

Check your progress

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