Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 3
Math
Unit 2
9th Grade
Lesson 3 of 22
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Lesson Notes
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Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.
The core standards covered in this lesson
HSS-ID.A.1 — Represent data with plots on the real number line (dot plots, histograms, and box plots).
The foundational standards covered in this lesson
6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
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
Suggestions for teachers to help them teach this lesson
In this lesson, students are asked to observe some differences between mean and median in a data set but will not need to be proficient at relating this to the skew of the data set until the end of lesson 4.Â
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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
The information in the table represents the number of single-family residential homes in Boston and their respective assessed value for fiscal year 2017.
Sketch a histogram based on the data in the table.
Property Assessment published by Department of Innovation and Technology is made available by Analyze Boston under the Open Data Commons PDDL. Accessed June 26, 2017, 2:31 p.m..
Identify which histograms belong with the measures of center shown. Explain your reasoning.
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
Each of the 20 students in Mr. Anderson’s class timed how long it took them to solve a puzzle. Their times, in minutes, are listed below.
Puzzle Times, accessed on June 21, 2017, 9:46 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.
Next
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.
Topic A: Descriptive Statistics in Univariate Data
Describe statistics. Represent data in frequency graphs and identify the center of a data set.
Standards
HSS-IC.A.1HSS-ID.A.1HSS-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.1HSS-ID.A.2
HSS-ID.A.1
HSS-ID.A.2HSS-ID.A.3
Calculate and interpret the spread (variance) of a data set.
HSS-ID.A.3HSS-ID.A.4
Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
HSS-ID.A.2HSS-ID.A.4
Interpret the standard deviation and interquartile range.
Calculate population percentages using the standard deviation.
HSS-ID.A.4
Given summary statistics, describe the best measures of center and spread. Describe reasoning.
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.1HSS-ID.A.2HSS-ID.A.3HSS-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.8HSS-ID.C.9
Determine the function of best fit and create a linear equation from least squares regression using technology.
HSS-ID.B.6aHSS-ID.B.6bHSS-ID.C.7
Use residuals to assess the strength of the model for a data set.
HSS-ID.B.6bHSS-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.6aHSS-ID.C.7HSS-ID.C.9
HSS-ID.B.6HSS-ID.C.7HSS-ID.C.8HSS-ID.C.9
HSS-ID.B.6HSS-ID.C.7HSS-ID.C.8HSS-ID.C.9N.Q.A.1
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