Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 4
Math
Unit 2
9th Grade
Lesson 4 of 22
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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.
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.
HSS-ID.A.3 — Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
The foundational standards covered in this lesson
6.SP.B.5 — Summarize numerical data sets in relation to their context, such as by:
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.
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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
How are these three graphs different?
Below is a histogram representing the total assessed property value of single-family houses in Boston during fiscal year 2017.
The graph does not include houses greater than $1,000,000 in assessed value. The descriptive data provided does include the houses greater than $1,000,000 in assessed value.
Approximate where you think the mean and the median would be based on the shape of the data.
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..
Below is a box plot of data that describes the amount of money spent per student on average, by state, in the school year 2004–2005.
Explain, is this data skew left, right, or symmetrical?
Box Plots, Amount Spent Per Student is made available by Shodor Education Foundation, Inc. on Shodor Interactivate. ©1994-2018 The Shodor Education Foundation, Inc. Accessed June 26, 2017, 2:37 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Each person in a random sample of ten ninth graders was asked one question:
Here are the data for these ten students:
Algebra I > Module 1 > Topic A > Lesson 2 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..
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
Calculate and interpret the spread (variance) of a data set.
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
Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.
HSS-ID.A.1
HSS-ID.A.2HSS-ID.A.3
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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