Curriculum / Math / 9th Grade / Unit 2: Descriptive Statistics / Lesson 6
Math
Unit 2
9th Grade
Lesson 6 of 22
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Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.
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.4 — Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
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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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Here is the formula for standard deviation.
Below are the definitions of the variables: • $${x }$$ represents a data item. • $${x_{i}}$$ represents EACH data item. • $${\mu }$$ represents the mean. • $${\sum }$$ represents the sum. • $${n }$$ is the number of data items. • $${\sigma }$$ is the standard deviation.
How would you describe the standard deviation using the definition of each variable?
Compare the following three graphs. Explain why the standard deviations are different. Describe the shapes of the graphs to explain your reasoning.
Mean: 6 Standard Deviation: 1.9
Mean: 6 Standard Deviation: 1.2
Mean: 6 Standard Deviation: 2.3
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Which data set has the smallest standard deviation of the three? The largest? Justify your answer.Â
Algebra I > Module 2 > Topic B > Lesson 5 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..
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Interpret the standard deviation and interquartile range.
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
HSS-ID.A.2HSS-ID.A.4
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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