Lesson 2 | Descriptive Statistics | 9th Grade Mathematics

Objective

Describe center and spread. Represent data in a box plot (box-and-whisker plot) and calculate the center and spread.

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.

Foundational Standards

The foundational standards covered in this lesson

6.SP.B.4

Statistics and Probability

6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
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

Understand that box plots are a way to organize univariate data, and identify the variable that the box plot is describing.
Describe center as a measurement of the middle of the data set. Median and mean are two measures of center.
Describe spread as how spread apart the data is in relation to the center. Interquartile range and standard deviation are the two measures of spread.
Create box plots using five number summaries consisting of the minimum, lower quartile, median, upper quartile, and maximum.
Identify the percentage of data that is located in each of the four quartiles, and analyze the box plot based on this information.
Describe that the middle 50% of the data is one measure of how spread out the data in the data set are. Define the range between the lower quartile and the upper quartile as the interquartile range.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

We are going to use what is known as the Moore and McCabe method for computing quartiles. This is where we DO NOT include the median in the calculation of the lower or upper quartiles.
Excel uses Tukey’s method, which includes the median when calculating both the lower and upper quartile in a data set with an odd number of items.
TI calculators use Moore and McCabe.
Students will need to understand how to create box plots efficiently, so this lesson reviews material from 6th grade. However, there is not a lot of practice on creating box plots by hand, so if your students need practice in this, be sure to build it in.

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Anchor Problems

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

Problem 1

Below is a dot plot of data showing the amount of time it takes students in Mr. S’s class to get to school.

Draw a line separating the upper half of the data and the lower half of the data.
Circle the median value.
Draw a line showing half of the upper half of the data and another showing half of the lower half of the data.
Estimate your box plot around the lines drawn in the dot plot.

Guiding Questions

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Problem 2

The plot below shows the results of a survey of households about the number of dogs they have.
Identify the following statements as true or false. Explain your reasoning in each case.

The maximum number of dogs per house is 8.
At least $${ \frac{1}{2} }$$ of the houses have 2 or more dogs.
All of the houses have dogs.
Half of the houses surveyed have between 2 and 4 dogs.
Most of the houses surveyed have no dogs.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 14 — Problem Set

Grade 6 Mathematics > Module 6 > Topic C > Lesson 14 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..

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

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

Problem 1

Consider the following box plots, which show the number of questions different students in three different classes got correct on a 20-question quiz.

What is the interquartile range of class 3?
What is the relationship between the median of each class data?
What is the relationship between the interquartile range of each class data?
How would you describe the comparison between the spread of data in each class?

References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 — Exercise 11–15

Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 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..

Modified by Fishtank Learning, Inc.

Problem 2

Given the following information, create a box plot and find the interquartile range.

For a large group of dogs, the shortest dog was 6 inches, and the tallest was 32 inches. One-half of the dogs were taller than 18 inches. One-fourth of the dogs were shorter than 15 inches. The upper quartile of the dog heights was 23 inches.

References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 — Exit Ticket

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.

Include problems that require students to make comparisons between box plots, as well as create box plots from raw data sets or from five number summaries.

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 14 — Independent Practice
EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 — Independent Practice
EngageNY Mathematics Algebra I > Module 2 > Topic A > Lesson 1 — Use the box plot questions for Independent Practice
EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 14 — Problem Set
EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic C > Lesson 15 — Problem Set
Yummy Math How Much Does It Cost to Make a Harry Potter Movie?

Lesson 1

Lesson 3

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

Foundational Standards

Statistics and Probability

Statistics and Probability

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem Set

Target Task

Problem 1

References

Problem 2

References

Additional Practice

Lesson Map

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