Lesson 10 | Descriptive Statistics | 9th Grade Mathematics

Objective

Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)

Common Core Standards

Core Standards

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).

Interpreting Categorical and Quantitative Data

HSS-ID.A.1 — Represent data with plots on the real number line (dot plots, histograms, and box plots).
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.

Interpreting Categorical and Quantitative Data

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).

Interpreting Categorical and Quantitative Data

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).
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.

Interpreting Categorical and Quantitative Data

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.

Foundational Standards

The foundational standards covered in this lesson

7.SP.A.1

Statistics and Probability

7.SP.A.1 — Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
7.SP.A.2

Statistics and Probability

7.SP.A.2 — Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
7.SP.B.3

Statistics and Probability

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

Statistics and Probability

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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Develop two statistical questions—one that requires categorical data and one that requires numerical data.
Define the variable you are measuring and relevant units, and explain why the variable represents either quantitative or categorical data.
Identify visual models you will use to illustrate the variables chosen. Identify the benefits and drawbacks of each visual model.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This is the first of three project-based lessons on univariate data. There is a second set of three project-based lessons on bivariate data at the end of this unit.
There is one basic context that is included in this series of three lessons, but the data sets can be swapped out easily using the resources in the problem set guidance or to meet the interests or needs of your students.
Experimentation and data collection is encouraged, although there are a lot of readily available data sets to use as well. Additional data sets and options are included in the problem set guidance.
The target task for this lesson is a reflection of the work done in class and is not meant to be an assessment of how well students have completed this part of the project.
The teacher will need to develop an appropriate rubric to emphasize the portions of the modeling cycle that are most relevant to their students’ development in this process. See the SIAM modeling guide, Math Modeling: Getting Started and Getting Solutions, for more information.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Below is a data set of the length of the arm span of a group of boys and another group of girls:

What statistical question could you answer using these data sets?

Guiding Questions

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References

STatistics Education Web (STEW) Grades 6-8, Armspans

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

What was challenging about developing a statistical question?
How did identifying the variables and choosing a visual representation help you to revise your statistical question?

Additional Practice

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.

Springboard, “19 Free Public Data Sets for Your First Data Science Project.”
Boston Indicators Project
Analyze Boston
Census at School: Teachers can sign up for this for free and enter in their class data. There is also a random sampler to gather real data from other participating classrooms.

MARS Formative Assessment Lessons for High School Interpreting Data: Muddying the Waters
STatistics Education Web (STEW) Grades 6-8, Bubble Trouble! — This activity requires science experimentation to collect data.

Lesson 9

Lesson 11

Lesson Map

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.

HSS-ID.A.2 HSS-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.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)

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 3/3)

HSS-ID.A.1 HSS-ID.A.2 HSS-ID.A.3 HSS-ID.A.4

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.

HSS-ID.B.5

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

Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 1/3)

HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9

Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 2/3)

HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9 N.Q.A.1

Develop and answer statistical questions through data analysis of existing data using appropriate statistical measures and displays. (Part 3/3)

HSS-ID.B.6 HSS-ID.C.7 HSS-ID.C.8 HSS-ID.C.9

Descriptive Statistics

Objective

Common Core Standards

Core Standards

Interpreting Categorical and Quantitative Data

Interpreting Categorical and Quantitative Data

Interpreting Categorical and Quantitative Data

Interpreting Categorical and Quantitative Data

Foundational Standards

Statistics and Probability

Statistics and Probability

Statistics and Probability

Statistics and Probability

Criteria for Success

Tips for Teachers

Anchor Problems

Guiding Questions

References

Target Task

Additional Practice

Lesson Map

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