Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 22
Math
Unit 2
9th Grade
Lesson 22 of 22
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Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)
The core standards covered in this lesson
HSS-ID.B.6 — Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
HSS-ID.C.7 — Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
HSS-ID.C.8 — Compute (using technology) and interpret the correlation coefficient of a linear fit.
HSS-ID.C.9 — Distinguish between correlation and causation.
The foundational standards covered in this lesson
8.SP.A.1 — Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.A.2 — Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.A.3 — Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
8.SP.A.4 — Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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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
Use the scatterplot, equation of the line of best fit, and correlation coefficient shown below to draw conclusions about your statistical question.
$${y=-4,443,755.85+244,351.32x}$$
$${r = 0.3940}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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
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.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)
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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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