Statistics: Investigate Patterns of Association in Bivariate Data Math B
Module #9 Student Edition Created in collaboration with Utah Middle School Math Project A University of Utah Partnership Project
San Dieguito Union High School District
Table of Contents MODULE 9: STATISTICS – INVESTIGATE PATTERNS OF ASSOCIATION IN BIVARIATE DATA STANDARDS FOR MATHEMATICAL PRACTICE: A GUIDE FOR STUDENTS AND PARENTS ............................................ 3
SECTION 9.1: CONSTRUCT AND INTERPRET SCATTERPLOTS FOR BIVARIATE DATA AND CONSTRUCT A LINEAR MODEL TO SOLVE PROBLEMS* ............................................................................................................................ 4 9.1A LESSON: READ AND INTERPRET A SCATTERPLOT* ........................................................................................ 5 9.1B LESSON: CREATE AND ANALYZE A SCATTERPLOT* ....................................................................................... 8 9.1C LESSON: LINES OF BEST FIT* .................................................................................................................... 12 9.1C EXTENSION: LAPTOP ................................................................................................................................ 17
SECTION 9.2: CONSTRUCT AND INTERPRET TWO-W AY FREQUENCY TABLES TO ANALYZE CATEGORICAL DATA* .... 18 9.2A LESSON: CONSTRUCT TWO-W AY FREQUENCY TABLES*.............................................................................. 19 9.2B LESSON: INTERPRET TWO-W AY FREQUENCY TABLES*................................................................................ 24 9.2B EXTENSION: CONDUCT A SURVEY.............................................................................................................. 27
* Denotes a lesson that was adapted from Utah Middle School Math Project © Utah Middle School Math Project & University of Utah http://utahmiddleschoolmath.org/ This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 Generic License http://creativecommons.org/licenses/by-nc/2.5/ This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License http://creativecommons.org/licenses/by-nc/3.0/legalcode
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Module 9: Statistics – Investigate Patterns of Association in Bivariate Data Online support for this module can be found at http://goo.gl/s2vDtM (case sensitive) or using the QR code below. This website includes copies of student lessons, homework, and instructional support videos.
Common Core Standard(s):
Construct and interpret scatterplots 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.1)
Curriculum Support Website
Know that straight lines are widely used to model relationships between two quantitative variables. For scatterplots 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.2)
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.3)
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. (8.SP.4)
Academic Vocabulary: Experiment, outcomes, sample space, random variables, realizations, quantitative (numerical) variables, categorical variables, univariate data, bivariate data, scatterplot, association, positive association, negative association, no apparent association, linear association, non-linear association, weak association, strong association, perfect association, cluster, outlier, line of best fit, linear model, prediction function, two-way frequency table, marginal frequencies, relative frequencies.
Module Overview: Up to this point, students have been studying data that falls on a straight line. Most of the time data given in the real world is not perfect; however, often the data is associated with patterns that can be described mathematically. In this module, students will investigate patterns of association in quantitative bivariate data by constructing and interpreting scatterplots, fitting a linear function to scatter plots that suggest a linear association, and using the function to solve problems and make predictions. In addition, they explore categorical bivariate data by constructing and interpreting two-way frequency tables.
Connections to Content: Prior Knowledge: Until 8th grade, the study of statistics has centered on univariate data. Students have created and analyzed univariate data displays, describing features of the data and calculating numerical measures of center and spread. In 8th grade, students have the opportunity to apply what they have learned about the coordinate plane and linear functions in order to analyze and interpret bivariate data and construct linear models for data sets that suggest a linear association. Future Knowledge: Students will more formally fit a linear, as well as additional types of functions, to bivariate data using technology. They will also calculate correlation coefficients, a numerical measure for determining the strength of a linear association. Students will also use residual plots as a tool for assessing the fit of a linear model. Students will also continue with the study of two-way frequency tables. SDUHSD Math B Module #9–STUDENT EDITION 2016-2017
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Standards for Mathematical Practice: A Guide for Students and Parents The Standards for Mathematical Practices are central to the Common Core. These practices build fluency and help students become better decision-makers and problem solvers. The practices reflect the most advanced and innovative thinking on how students should interact with math content. Students and parents will develop skill with these standards by asking some of these questions: Make Sense of Problems and Persevere in Solving Them. What is the problem that you are solving for? Can you think of a problem that you recently solved that is similar to this one? How will you go about solving the problem?(i.e. What’s your plan?) Are you progressing towards a solution? How do you know? Should you try a different solution plan? How can you check your solution using a different method? Construct Viable Arguments and Critique the Reasoning of Others. Can you write or recall an expression or equation to match the problem situation? What do the numbers or variables in the equation refer to? What’s the connection among the numbers and variables in the equation? Reason Abstractly and Quantitatively. Tell me what your answers(s) mean(s) How do you know that your answer is correct? If I told you I think the answer should be (a wrong answer), how would you explain to me why I’m wrong? Model with Mathematics. Do you know a formula or relationship that fits this problem situation? What’s the connection among the numbers in the problem? Is your answer reasonable? How do you know? What do(es) the number(s) in your solution refer to? Use Appropriate Tools Strategically. What tools could you use to solve this problem? How can each one help you? Which tool is most useful for this problem? Explain your choice. Why is this tool (the one selected) better to use than (another tool mentioned)? Before you solve the problem, can you estimate the solution? Attend to Precision. What do the symbols that you used mean? What units of measure are you using (for measurement problems) Explain to me what (term from the lesson) means. Look For and Make Use of Structure. What do you notice about the answers to the exercises you’ve just completed? What do different parts of the expression or equation you are using tell you about possible correct answers? Look for and Express Regularity in Repeated Reasoning. What shortcut can you think of that will always work for these kinds of problems? What pattern(s) do you see? Can you make a generalization?
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Section 9.1: Construct and Interpret Scatterplots for Bivariate Data and Construct a Linear Model to Solve Problems* Section Overview: In 7th grade, students studied univariate data. In this section, students focus on bivariate data, specifically quantitative or numerical data. This section begins with a problem that deals with univariate data and then uses the same context to explore a bivariate data set. As in the case of univariate data, analysis of bivariate measurement data graphed on a scatterplot proceeds by describing shape, center, and spread. In this section, students learn how to construct, read, and interpret a scatterplot, investigate and describe trends and patterns of association between two variables, and interpret these associations in a variety of real-world situations. For scatterplots that suggest a linear association, students informally fit a straight line to the data and assess the model fit by judging the closeness of the data points to the line. They also analyze how outliers affect a line of best fit and reason about whether to drop outliers from a data set. Students then construct functions to model the data sets that suggest a linear association and use the functions to make predictions and solve real-world problems, noting that limitations exist for extreme values of x. Students interpret the slope and y-intercept of the prediction function in context. Throughout the section, students must use a critical eye, keeping in mind that most statistical data is subjective and has limitations.
Concepts and Skills to be Mastered: By the end of this section students should be able to:
Read, interpret, and construct a scatterplot for bivariate data. Describe patterns of association in a scatterplot. Draw a line of best fit for linear models. Informally assess the model fit by judging the closeness of the data points to the line. Write a prediction function for the line of best fit. Explain the meaning of the slope and y-intercept of the prediction function in context. Use the prediction function of a linear model to solve problems.
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9.1A Lesson: Read and Interpret a Scatterplot* Name: 1. Jenny is a hair stylist and decides to record the amount of money she makes in tips over a 10-day period. She wonders if the amount she earns in tips is associated with the number of clients she has each day. She looks back through her appointment book and records the information in the table of values. To better visualize the data, Jenny makes a scatterplot of the data. A scatterplot is a graph in the coordinate plane of the set of all (x,y) ordered pairs that shows the relationship between two sets of data. a. What does the point (9, 100) represent in the context?
Period: Number of Clients 8 12 11 9 6 8 9 10 3 11
Amount of Money Made in Tips ($) 75 100 115 100 55 90 75 105 105 100
b. What observations can you make about the scatterplot?
c. Is the amount Jenny earns in tips associated with the number of clients she has each day? Explain.
Univariate data is data that represents collections or measurements of one variable. The scatterplot above compares bivariate data. Bivariate data is data that has two variables. Scatterplots are often used to represent bivariate data so that the relationship (if any) between the variables is easily seen. Directions: Determine if the following scenarios represent univariate or bivariate data. 2. Lucas conducts an experiment where he records the number of speeding tickets issued in Iron County in a given year along with the average price of gasoline for that same given year. He collects this data from the year 1990 through 2015.
3. Lea conducts an experiment where she records the heights of all the NBA basketball players on the LA Lakers roster for the 2014 season.
4. Adele conducts an experiment where she records the selling price of several homes in a neighborhood. 5. Lisa conducts an experiment on the number of times a person works out a week and the person’s weight.
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6. Define the following terms. a. Experiment: b. Sample space: c. Random variables: d. Cluster: 7. Izumi is the score keeper for her school’s basketball team and records game statistics. She records number of field goals, number of field goals attempted, number of assists, and number of rebounds. The table below shows the number of field goals attempted and the number of field goals made. As Izumi examines the data, she questions, “Is there is an association between the number of field goals made and the number of field goals attempted?” Izumi creates a scatterplot of the data.
Casey Corbin Monique Ortiz Maria Ferney Amelia Krebs Tonya Smith Juanita Martinez Sara Garcia Alicia Mortenson Parker Christiansen Rachel Reagan Paula Lyons Thao Ho Jessica Geffen
Field Goals Attempted 368 102 91 310 56 58 151 67 94 183 276 221 127
Field Goals Made 134 36 32 137 25 17 61 26 29 66 108 94 54
140 120 Field Goals Made
Player
100 80 60 40 20 0
50 100 150 200 250 300 350 400 Field Goals Attempted
a. Izumi did not plot the data for the last two players in the table, Thao Ho and Jessica Geffen. Plot the data for these players on the scatterplot and label the points with these players’ initials. b. What observations can you make about the data Izumi collected in the table?
c. Using the scatterplot, determine if there is a relationship between field goals attempted and field goals made. Describe any trends or patterns you observe in the data.
d. Can you think of another variable, that when graphed with the number of field goals made, would have a positive association?
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8. In addition to data about field goals, Izumi is curious about the relationship between the number of assists and the number of rebounds a player makes in a season. In order to study this relationship, Izumi gathers the following data and creates a scatterplot. Assists 6 50 89 25 70 3 100 33 64 45 59 15 30
Rebounds 170 54 42 193 39 26 73 152 93 67 117 179 113
200 175
Number of Rebounds
Player Casey Corbin Monique Ortiz Maria Ferney Amelia Krebs Tonya Smith Juanita Martinez Sara Garcia Alicia Mortenson Parker Christiansen Rachel Reagan Paula Lyons Thao Ho Jessica Geffen
150 125 100 75 50 25 0
10 20 30 40 50 60 70 80 90 100 Number of Assists
a. Which player does the circled data point represent? b. Izumi notices the circled data point stands out noticeably from the general behavior of the data set. What is this point called? Provide an explanation as to why this player’s data does not fit with the rest of the data.
c. Using the scatterplot, determine if there is a relationship between number of assists and number of rebounds. Describe any trends or patterns you observe in the data.
d. Can you think of another variable, that when graphed with the number of field goals made, would have a negative association?
9. Which data set appears to have a stronger association: the relationship between number of field goal made and number of field goal attempts or the relationship between number of rebounds and number of assists? Explain your reasoning.
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9.1B Lesson: Create and Analyze a ScatterPlot* Name:
Period:
1. As we study bivariate data, we have seen data sets that show different types of association between two variables. There are many ways that we can describe the association (if there is one) between two variables. Label the scatterplots below with the linear association it represents. Label each axis with an independent and dependent variable that could represent the association. a.
b.
c.
2. Do you anticipate an association between a person’s height and his or her shoe length? If so, make a prediction.
3. Record the information you collected in homework 9.1A in the table below. Fill in the rest of the table by collecting additional data from your classmates. a. Which variable is independent? Which variable is dependent?
Height
Shoe Length
1. 2. 3. 4. 5.
b. If the data in the table was graphed, should feet or inches be used to represent height? Justify your answer.
6. 7. 8. 9. 10.
c. When conducting an experiment, why is it important to use a random sample of data?
11. 12. 13. 14. 15.
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d. Make a scatterplot of the data. Label each axis. e. Examine your scatterplot. Is there an association between a person’s shoe length and height? Explain. Describe any trends or patterns you observe in the data including clusters and outliers.
f. What other variables are likely to have a positive association with a person’s height or shoe length?
4. When is a linear association considered strong? Draw an example.
5. When is a linear association considered weak? Draw an example.
6. When is a linear association considered perfect? Draw an example.
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Directions: Describe the association between x and y using the terms from the previous page. Circle any clusters in the data. Put a star by any points that appear to be outliers. 7.
8.
9.
10.
11.
12.
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Directions: Examine the following scatterplots. Describe the association between the two variables. Circle any clusters in the data. Put a star by any points that appear to be outliers. Use the context to give possible explanations as to why these trends, patterns, and associations exist. 13. The scatterplot given below shows the temperature of a cup of tea sitting on the counter for 30 minutes. The cup of tea is sitting in a room that is 70 degrees.
Temperature (F)
20 0
16 0
12 0
8 0
4 0
0
4
8
12
16
20
24
28
32
36
40
Time (minutes)
14. The Paradise Pool records the average daily temperature and the number of visitors to their pool for 18 days throughout the month of July. On July 24th, to celebrate Pioneer Day, admission is half off. The average daily temperature on that day is 90 degrees. Visitors vs. Temperature at a Swimming Pool 600 550 500 450
Visitors
400 350 300 250 200 150 100 50 0
10
20 30 40 50 60 70
80 90 100 110
Average Daily Temperature (F)
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9.1C Lesson: Lines of Best Fit* Name:
Period:
Most real-world data does not fall perfectly on a line. However, if the data on a scatterplot resembles a line, we can fit a line to the data, write a function for the line, and use this function to solve problems and make predictions. The line that you use to represent the data is called the line of best fit. We will refer to the function you write for the line of best fit as the prediction function. The most common way to find the line of best fit is to draw a straight line through the center of a group of data points plotted on a scatterplot, having some points above the line and some points below. 1. Examine the scatterplot to complete the following. a. State the association. Explain.
y 8 7
b. Using a ruler, draw a line of best fit through the data points that captures the general trend of the data.
6
c. Estimate the slope and y-intercept of your line.
4
5
3 2
1
d. Write a prediction function for the data set.
e. Use your prediction function to find the value of
f. Use your prediction function to find the value of
0
when
when
2
4
6
8 10 12 14 16 18 20
x
. Write your values as an ordered pair.
. Write your values as an ordered pair.
g. Examine the scatterplot. Does it support the coordinates you found in parts e and f?
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2. Examine the scatterplot to complete the following.
y
a. State the association. Explain
9 8
b. Using a ruler, draw a line of best fit through the data points that captures the general trend of the data.
7 6 5 4
c. Estimate the slope and y-intercept of your line.
3 2
1 d. Write a prediction function for the data set. 0
e. Use your prediction function to find the value of
when
f. Use your prediction function to find the value of
when
2
4
6
8
10
12
14
x
.
.
g. Examine the scatterplot. Does it support the coordinates you found in parts e and f?
3. The scatterplot shows the weight, in pounds, of a professional wrestler who is on a strict diet. a.
Using a ruler, draw a line of best fit through the data points that captures the general trend of the data.
b.
Estimate the slope and y-intercept of your line.
c.
Write a prediction function for the data set.
d.
What does the slope represent in the context?
e.
What does the y-intercept represent in the context?
f.
Predict this person’s weight after 18 weeks if this trend continues. Is this value realistic?
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4. In lesson 9.1A, Izumi collected basketball statistics and created the scatterplot below comparing the number of field goals made and field goals attempted. a. What is the association between the number of field goals attempted and the number of field goals made? Is the association strong or weak? Justify your answer.
b. Draw a line of best fit on the scatterplot.
c. Write a prediction function for the line of best fit you drew.
d. What does the slope represent in the context?
e. What does the y-intercept represent in the context?
f. Use your prediction function to predict the number of field goals a person would make if he attempted 102 field goals.
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5. Software programs and graphing calculators can be used to draw lines of best fit. Izumi used a graphing calculator to generate a line of best fit for her data on assists and rebounds. The graph to the right shows the line of best fit generated by the calculator. After creating this line of best fit, Izumi decided that it might be best to drop the outlier (3, 26) from her data set because this data represents a player that joined the team midway through the season. After dropping the outlier, Izumi used a calculator to generate a new line of best fit. a. Analyze the differences in the two lines. What did the outlier do to the line of best fit generated by the calculator?
b. Write a prediction function for the line of best fit generated by the calculator with the data set that does not include the outlier.
c. What does the slope represent in the context?
d. What does the y-intercept represent in the context?
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e. Use your function to predict the number of rebounds random players would have if they made 110 assists throughout the season? 150 assists? Explain the limitations that the data exhibits.
f.
Use your function to predict the number of assists random players would have if they made 150 rebounds throughout the season. .
6. Which scatterplot, the Field Goals Made vs. Field Goals Attempts or Rebounds vs. Assists, is more closely aligned with its line of best fit? Justify your answer. What does this tell us about the strength of each of the associations? What does this tell us about the accuracy of using each of the prediction functions to make predictions?
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9.1C Extension: Laptop Name:
Period:
Spencer forgot to plug in Toby’s laptop. Toby was hoping to take his laptop with him to work with a full battery. The pictures below show screenshots of the battery charge indicator after he plugs in his computer at 9:11 am 1. What are the two variables in this situation? Explain the association between the two variables.
2. Make a scatterplot of the data. Label and scale each axis.
3. On your scatterplot, draw a line of best fit and find the equation of your line.
4. When can Toby expect to have a fully charged battery?
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Section 9.2: Construct and Interpret Two-Way Frequency Tables to Analyze Categorical Data* Section Overview: At the beginning of this section, students are introduced to a new type of random variable – a categorical random variable. Up to this point, students have been studying quantitative random variables. Quantitative random variables have a cardinal numerical value. Categorical random variables are those that represent some quality or name. Categorical data is often represented and summarized in a two-way frequency table. In this section, students learn what a two-way frequency table is and how to read it. They complete two-way frequency tables by filling in missing data. As the section progresses, students begin to formally interpret the frequency tables. They calculate and analyze relative frequencies (for rows, columns, and the entire table) to describe possible associations between the two variables and use these associations to make decisions. Finally, students conduct a survey of their own involving categorical random variables, summarize their data in a two-way frequency table, and analyze the data to determine if an association exists between the two variables of interest.
Concepts and Skills to be Mastered: By the end of this section students should be able to: Read and understand a two-way frequency table. Construct a two-way frequency table for categorical data. Calculate and analyze relative frequencies (for rows, columns, and the entire table) to describe possible associations between the two variables and to make decisions.
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9.2A Lesson: Construct Two-Way Frequency Tables* Name:
Period:
1. Bivariate data can be represented as quantitative or categorical random variables. a. Random Variables: .
b. Quantitative Variables:
c. Categorical Variables:
2. State if the following variables are quantitative or categorical. a. Gender of babies born at Palomar Hospital in June b. Thickness of plastic for various types of water bottles c. Favorite ice cream, choosing between chocolate, vanilla, or strawberry d. The number of pages you can read in your favorite book before you fall asleep In the previous section, we summarized and displayed quantitative data using a scatterplot. In this section, we will summarize and display categorical bivariate data using a two-way frequency table. A two-way frequency table is “two-way” because each bivariate data entry is composed of an ordered pair from two categorical random variables. 3. Jessie enjoys spending time at the mall with her friends. Sometimes, her friends can’t join her because they have chores at home or their parents gave them a curfew. She notices that it tends to be the same group of friends who have curfews on school nights who also have chores to do at home. Jessie wonders, “In general, do students at my school who have chores at home also have curfews at night?” Jessie conducts an experiment and randomly surveys 52 students at her school, asking if they have a curfew and if they have household chores. She organizes her findings into a two way frequency table. Use the table to answer the questions below. a. How many students have a curfew and have chores? b. How many students have no curfew and have chores?
Has A Curfew
No Curfew
Has Chores
26
9
No Chores
5
12
Total
Total c. How many students have no curfew and no chores? The frequencies found within the body of a two-way table are called joint frequencies. The values found above are joint frequencies. SDUHSD Math B Module #9–STUDENT EDITION 2016-2017
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It is also possible to calculate the frequencies for “Total” column and “Total” row. These frequencies represent the total count of one variable at a time. These frequencies are called marginal frequencies because they are located in the margins of the table. d. Find the frequencies for the Total column and Total row by adding up the numbers in each column and row. Write these numbers in the table. e. How many of the students surveyed have chores? f. How many of the students surveyed have a curfew? g. Add the entries in the Total row and the Total column and put this number in the cell in the bottom right corner. Does this number match how many students Jessie said she was going to survey? 4. Maddie loves to eat tomatoes from her garden in San Diego. She asked her friend Renzo, “Don’t you just love tomatoes?” Renzo crinkled his nose and replied, “Ew, tomatoes gross me out! When I see them in the grocery store, I just keep on walking.” Renzo’s response prompted Maddie to think, “I don’t buy tomatoes at the grocery store either, because I grow them in my garden. The tomatoes from my garden are delicious, whereas grocery store tomatoes look less appealing to me. I wonder if there is an association between enjoying tomatoes and having a garden at home.” She decides to survey 100 randomly selected San Diego vegetable-eating residents and asks each of them two questions:
Do you primarily obtain your vegetables at the grocery store, the farmer’s market, or your home garden?
Do you like tomatoes?
Maddie summarized her results in the two-way table. Grocery Store
Farmer’s Market
Home Garden
Likes Tomatoes
50
4
12
Dislikes Tomatoes
30
1
3
Total
Total
a. Fill in the marginal frequencies for the Total column and Total row in the table. b. Check to make sure that you found the above frequencies correctly by finding the total number of people surveyed. c. How many people get their tomatoes at the farmer’s market and dislike tomatoes? d. How many people get their tomatoes from a home garden and like tomatoes? e. How many people get their tomatoes from the grocery store? f.
How many people like tomatoes?
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5. Use the given information to complete the two-way frequency table about the eating habits of 595 students at Copper Ridge Middle School.
190 male students eat breakfast regularly out of 320 total males surveyed. 295 students do not eat breakfast regularly 165 females do not eat breakfast regularly
Fill in the missing information in the table and then answer the questions below. Round to the nearest tenth of a percent, when necessary.
Male
Female
Total
Eat breakfast regularly Do not eat breakfast regularly Total
a. How many females total were surveyed?
b. How many people surveyed eat breakfast regularly?
c. How many people total were surveyed?
d. How many males surveyed do not eat breakfast regularly?
e. How many females surveyed eat breakfast regularly?
f.
What percentage of the total number of people surveyed eat breakfast regularly?
g. What percentage of the females surveyed eat breakfast regularly?
h. What percentage of the people who eat breakfast regularly are male?
i.
What percentage of the total number of people surveyed are females who do not eat breakfast regularly?
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6.
The data in the table represents modes of transportation to and from Brookside High School. Fill in the missing information in the table and answer the questions below. Round to the nearest tenth of a percent, when necessary.
Walk
Car
Male Female
Bus
Cycle
28 46
Total
45
Total 129
12
17
27
69
92
a. How many males ride their bikes to school? b. How many females take the bus to school? c. How many females were surveyed? d. How many students were surveyed? e. What percentage of the total number of people surveyed walk to school?
f. What percentage of the total number of people surveyed are females that bike to school?
g. What percentage of the males surveyed cycle to school?
7. Jason collects data about the number of people who own a smart phone and if they also own an MP3 player. He gets the following information: 25 people surveyed owned smart phones 20 people that own a smart phone do not own an MP3 player 9 people do not own smart phones but they do own an MP3 player 24 people do not own an MP3 player Design and complete a two-way frequency table to represent the data.
38
a. How many people did Jason survey? b. How many people own a smart phone and an MP3 player? c. How many people own an MP3 player?
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8. Emily wondered if there is an association between age and favorite flavor of ice cream (choices: chocolate, strawberry, and vanilla). She surveyed 200 children in different age ranges. Emily gets the following information:
of the children surveyed chose chocolate as their favorite flavor
25% of the children surveyed were in the age range of 8 – 12 years old
of the children surveyed were in the age range of 13 – 17 years old
50% of the children in the age range of 3 – 7 years old chose chocolate as their favorite flavor 50 children chose strawberry as their favorite flavor
The table below shows the results of her survey. Complete the two-way frequency table. Chocolate
Vanilla
Strawberry
Total
Ages 3 to 7 Ages 8 to 12
25
Ages 13 to 17
12 12
Total
200
Use numerical evidence from your table to answer the questions below: a. Emily is in charge of buying ice cream for a pre-school carnival. Which type or types of ice cream should she purchase?
b. Emily is in charge of buying ice cream for a neighborhood picnic at which all ages of children will attend. What type or types of ice cream should she buy?
c. True or false, children in all of the age ranges have an equal likelihood of choosing chocolate. Use numerical evidence to justify your answer.
d. True or false, children in the age ranges of 8 to 12 and 13 to 17 both have an equal likelihood of choosing strawberry. Use numerical evidence to justify your answer.
e. True or false, as students get older, they tend to like vanilla more. Use numerical evidence to justify your answer.
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9.2B Lesson: Interpret Two-Way Frequency Tables* Name:
Period:
1. The table below displays the data Tracy and Paul gathered on gender and the type of movie a person prefers. Use numerical evidence from the table to answer the questions below. Romance
Comedy
Action
Drama
Totals
Male
15
77
100
28
220
Female
80
98
50
52
280
Total
95
175
150
80
500
a. Tracy is showing a movie at a party at which males and females will be present. Which type or types of movies should Tracy show? Justify your answer.
b. Paul is showing a movie at a party at which only males will be present. Which type or types of movies should Paul show? Justify your answer.
c.
Tracy is showing a movie at a party at which only females will be present. Which type or types of movies should Tracy show? Justify your answer.
d. Do both males and females have an equal likelihood of choosing comedy movies? Use numerical evidence to justify your answer.
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2. The table displays the data Jessie gathered on student curfews and household chores.
Has A Curfew
No Curfew
Totals
Has Chores
26
9
35
No Chores
5
12
17
Totals
31
21
52
a. Analyze the two-way table. What arguments can you make about the data? Use numerical evidence to support your answer.
b. Is there an association between kids having chores and having a curfew? Use numerical evidence to support your answer.
3. The table displays the data Maddie gathered on liking tomatoes and having a home garden. Grocery Store
Farmer’s Market
Home Garden
Totals
Likes Tomatoes
50
4
12
66
Dislikes Tomatoes
30
1
3
34
Totals
80
5
15
100
a. Analyze the two-way table. What arguments can you make about the data? Use numerical evidence to support your answer.
b. Is there an association between growing your own tomatoes and whether or not you like tomatoes? Use numerical evidence to support your answer.
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4. The table displays the data gathered about the eating habits of 595 students at Copper Ridge Middle School. Is there an association between gender and whether or not a person eats breakfast regularly? Use numerical evidence to support your answer.
Male
Female
Totals
Eat breakfast regularly
190
110
300
Do not eat breakfast regularly
130
165
295
Totals
320
275
595
5. Joy wanted to determine whether there is an association between gender and whether or not a person has pierced ears. She collected data from a random sample of young adults ages 13 to 18. Is there an association between gender Has Pierced Ears Does not have Pierced Ears Totals and whether or not they have Male 90 19 71 their ears pierced? Use numerical evidence to support Female 88 84 4 your answer. Totals
103
75
178
(problem #5 is adapted from illustrativemathematics.org)
6. All the students at Rydell Middle School were asked to identify their favorite academic subject and whether they were in 7th or 8th grade. The results are shown in the table. Is there an association between favorite academic subject and grade for students at Rydell? Use numerical evidence to support your answer.
Favorite Subject by Grade Grade
English
History
Math/Science
Other
Totals
7th Grade
38
36
28
14
116
8th Grade
47
45
72
18
182
Totals
85
81
100
32
298
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9.2B Extension: Conduct a Survey Name:
Period: task adapted from illustrative mathematics
Is there an association between whether a student plays a sport and whether he or she plays a musical instrument? To investigate these questions, ask 20 students in your class to answer the following two questions: 1. Do you play a sport? (yes or no) 2. Do you play a musical instrument? (yes or no) Record answers in the table below. Student Name
Sport
Musical Instrument
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Summarize the data into a clearly labeled frequency table.
Directions: Use the table that you made above to answer the following questions. 1. What percentage of students play a sport and a musical instrument?
2. What percentage of students who play a sport also play a musical instrument?
3. What percentage of students who do not play a sport play a musical instrument?
4. What percentage of musical instrument players do not play a sport?
5. Based on the class data, do you think there is an association between playing a sport and playing an instrument? Use numerical evidence to support your answer.
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