Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 9
Math
Unit 2
9th Grade
Lesson 9 of 22
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Given summary statistics, describe the best measures of center and spread. Describe reasoning.
The core standards covered in this lesson
HSS-ID.A.2 — Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
The foundational standards covered in this lesson
7.SP.B.3 — Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4 — Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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This lesson provides students with focused practice on all of the skills they will need to complete the project in lessons 10–12.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A science museum has a “Traveling Around the World” exhibit. Using 3-D technology, participants can make a virtual tour of cities and towns around the world. Students at Waldo High School registered with the museum to participate in a virtual tour of Kenya, visiting the capital city of Nairobi and several small towns. Before they take the tour, however, their mathematics class decided to study Kenya using demographic data from 2010 provided by the US Census Bureau. They also obtained data for the United States from 2010 to compare to data for Kenya. The following histograms represent the age distributions of the two countries.
Algebra I > Module 2 > Topic B > Lesson 8 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..
A random sample of 200 people from Kenya in 2010 and a random sample of 200 people from the United States were available for study. Box plots constructed using the ages of the people in these two samples are shown below.
Describe the center, spread, and shape of each graph.
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A statistically-minded state trooper wondered if the speed distributions are similar for cars traveling northbound and for cars traveling southbound on an isolated stretch of interstate highway. He uses a radar gun to measure the speed of all northbound cars and all southbound cars passing a particular location during a 15-minute period. Here are his results:
Draw box plots of these two data sets, and then use the plots and appropriate numerical summaries of the data to write a few sentences comparing the speeds of northbound cars and southbound cars at this location during the fifteen-minute time period.
Speed Trap, accessed on June 21, 2017, 10:37 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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.
Lesson 8
Lesson 10
Topic A: Descriptive Statistics in Univariate Data
Describe statistics. Represent data in frequency graphs and identify the center of a data set.
HSS-IC.A.1 HSS-ID.A.1 HSS-ID.A.2
Describe center and spread. Represent data in a box plot (box-and-whisker plot) and calculate the center and spread.
HSS-ID.A.1 HSS-ID.A.2
Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.
HSS-ID.A.1
Describe the shape of the data in box plots and histograms. Choose an appropriate measure of center (or an appropriate shape) based on the shape and the relationship between the mean and the median.
HSS-ID.A.2 HSS-ID.A.3
Calculate and interpret the spread (variance) of a data set.
HSS-ID.A.3 HSS-ID.A.4
Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
HSS-ID.A.2 HSS-ID.A.4
Interpret the standard deviation and interquartile range.
Calculate population percentages using the standard deviation.
HSS-ID.A.4
HSS-ID.A.2
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)
HSS-ID.A.1 HSS-ID.A.2 HSS-ID.A.3 HSS-ID.A.4
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 2/3)
Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)
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Topic B: Descriptive Statistics in Bivariate Data
Define categorical and numerical data. Create two-way tables to organize bivariate categorical data.
HSS-ID.B.5
Describe relative and relative conditional frequencies of two-way tables.
Create scatterplots and identify function shapes in scatterplots.
HSS-ID.B.6
Calculate, with technology, the correlation coefficient for a data set. Explain why correlation does not determine causation.
HSS-ID.C.8 HSS-ID.C.9
Determine the function of best fit and create a linear equation from least squares regression using technology.
HSS-ID.B.6a HSS-ID.B.6b HSS-ID.C.7
Use residuals to assess the strength of the model for a data set.
HSS-ID.B.6b HSS-ID.B.6c
Describe the relationship between two quantitative variables in a contextual situation represented in a scatterplot using the correlation coefficient, least squares regression, and residuals as evidence.
HSS-ID.B.6a HSS-ID.C.7 HSS-ID.C.9
HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9
HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9 N.Q.A.1
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