Curriculum / Math / 6th Grade / Unit 8: Statistics / Lesson 9
Math
Unit 8
6th Grade
Lesson 9 of 14
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Lesson Notes
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Use the range and interquartile range to understand the spread and variability of a data set.
The core standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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?
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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.
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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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.
Next
Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.
Topic A: Understanding Statistics & Distributions
Define and identify statistical questions.
Standards
6.SP.A.16.SP.B.5.A
Describe data that is represented in a dot plot. Represent data using dot plots and frequency tables.
6.SP.B.46.SP.B.5.A
Represent data using histograms.
6.SP.B.4
Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.
6.SP.A.2
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Topic B: Measurements of Center & Variability
Define and determine the mean of a data set.
6.SP.A.26.SP.B.5.C
Define and determine the median of a data set.
Define and determine the mode of a data set.
Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.
6.SP.A.26.SP.B.5.D
6.SP.B.5.C
Compare measures of center and measures of spread to describe data sets.
6.SP.A.3
Topic C: Box Plots & Circle Graphs
Represent data using box plots.
6.SP.B.46.SP.B.5
Analyze box plots and other representations, and summarize numerical data in context.
Analyze circle graphs in context.
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