Statistics

Lesson 9

Math

Unit 8

6th Grade

Lesson 9 of 14

Objective


Use the range and interquartile range to understand the spread and variability of a data set.

Common Core Standards


Core Standards

  • 6.SP.A.2 — Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
  • 6.SP.B.5.C — Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Criteria for Success


  1. Understand that the quartiles of a data set divide the data into equal quarters with approximately 25% of the data falling in each quartile. 
  2. Find the lower quartile and upper quartile of a data set.
  3. Understand that the range and interquartile range of a data set provide information about the spread or variability of a data set.
  4. Find the range and interquartile range of a data set.

Tips for Teachers


This lesson introduces the concept of variability and spread by looking at the range and quartiles of a data set. In the next lesson, students will investigate and understand the mean absolute deviation as another measure of variability.

Lesson Materials

  • Number strips (1 per student) — These require some cutting, which can either be done prior to the lesson or during the lesson if scissors are provided to the students. Note, the same strips are used for both Lesson 6 and Lesson 9.
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Anchor Problems


Problem 1

Recall the Anchor Problem you worked with from Lesson 6 of this unit, about the temperatures in March. 

For Paper Strip A: Temperatures of the first 11 days in March
24    35    64    60    35    21    31    38    49    57    50

For Paper Strip B: Predicted temperatures of the last 10 days in March
50    49    49    49    49    48    48    46    46    48

a.   Refold each paper strip in half so that half of the temperatures are on the left side and half of the temperatures are on the right side. What data point did you just find?

b.   Fold each half of the strips in half again to create fourths or quarters. What percent or fraction of the data set is represented in each section of the strip?

c.   Define and name the lower quartile, median, and upper quartile temperatures for the first 11 days of March and the last 10 days of March. 

d.   Find the range and interquartile range of temperatures for the first 11 days of March and for the last 10 days of March.

e.   What do the range and interquartile range tell you about the variability and spread of the data set?

Guiding Questions

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Problem 2

Two brands of chips advertise the same serving size and approximate number of chips in the bag. You count the number of chips in a sample of 12 bags for each brand and record the data below.

Brand X: 
36  38   38   38   40   42   42   44   44   45   48   49

Brand Y:
39   39   39   39   40   40   40   40   40   41   41   43

Which brand has less variability in the number of chips per bag? Justify your answer using data from the set. 

Guiding Questions

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Problem 3

Three dot plots are shown below.

Use the information shared below to determine which dot plot matches the situation. 

a.   You know the median of the data set is 4. Can you determine which dot plot represents the data set? Why or why not?

b.   You also know the range of the data set is 6. Now can you determine which dot plot represents the data set? Why or why not?

c.   You determine that the interquartile range of the data set is 4. Does this new information help you narrow in on which dot plot represents the data set?

d.   For the other two dot plots, determine the lower quartile, the upper quartile, and the interquartile range of the data set.

Guiding Questions

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Problem Set

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Target Task


The dot plot below represents salaries, in thousands of dollars, of students graduating with a Master’s degree from a graduate school.

a.   Find the lower quartile, median, upper quartile, range, and interquartile range of salaries.

b.   Explain how the interquartile range helps you understand the spread of the data set.

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 8

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Lesson 10

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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