Statistics

Lesson 13

Math

Unit 8

6th Grade

Lesson 13 of 14

Objective


Analyze box plots and other representations, and summarize numerical data in context.

Common Core Standards


Core Standards

  • 6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • 6.SP.B.5 — Summarize numerical data sets in relation to their context, such as by:

Criteria for Success


  1. Draw conclusions about a data set by analyzing a box plot.
  2. Compare box plots of different data sets.

Tips for Teachers


This Boxplot Grapher by IMathAS is a good tool to create box plots.

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Anchor Problems


Problem 1

Lorna is interested in knowing the typical length of a movie. She randomly selects some movies and records their length, in minutes. She determines the following five-number summary for the data set:

Minimum: 75

Lower quartile: 90

Median: 110

Upper quartile: 120

Maximum: 135

a.   Draw a box plot to represent the data.

b.   What questions could you ask about the data shown in the box plot? 

c.   Sketch a dot plot that could represent the data set.

Guiding Questions

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Problem 2

Ninety-four people were asked to grab as many Tootsie Pops as they could hold. Here is a box plot for this data. Use it to answer the questions that follow.

a.   What might explain the variability in the number of Tootsie Pops grabbed by the 94 people?

b.   Determine the five-number summary of the data set.

c.   What is the range of number of Tootsie Pops that the middle 50% of people grabbed?

d.   Answer True or False for the following statements:

  1. More people grabbed between 22–42 Tootsie Pops than between 20–22 Tootsie Pops.
  2. The same number of people grabbed between 7–18 Tootsie Pops as people who grabbed between 18–20 Tootsie Pops. 
  3. About 50% of the people grabbed between 22–42 Tootsie Pops.
  4. The average number of Tootsie Pops grabbed was between 18–22.
  5. It must be true that at least one person grabbed 42 Tootsie Pops.
  6. It must be true that at least one person grabbed 20 Tootsie Pops.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 15Example 1

Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

At the end of the year, a middle school held a trivia competition. Each grade had the same number of teams compete, and each team answered the same 20 questions. The box plots below show the results of how the teams scored in each grade.

a.   Name one observation of how the data of all three classes are the same.

b.   Name one observation of how 6th Grade and 7th Grade are different.

c.   Name one observation of how 6th Grade and 8th Grade are different.

d.   Which grade do you think performed the best in the trivia competition? Explain your reasoning.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 15Exercises 11-15

Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


A veterinarian’s office collects data on the weights of cats that are brought into their office. The box plot below shows these data. 

Which of the following statements are true? If the statement is false, modify it to make the statement true.

a.   At least one cat weighs 11 pounds.

b.   At least one cat weighs 14 pounds.

c.   About 75% of the cats weigh 12 or more pounds.

d.   About half of the cats weigh between 14 and 19 pounds.

e.   There are more cats that weigh between 19 and 22 pounds than there are cats that weigh between 11 and 12 pounds.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 12

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Lesson 14

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Statistics & Distributions

Topic B: Measurements of Center & Variability

Topic C: Box Plots & Circle Graphs

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