Teacher Note: What to print For this lesson, you can print: Homework Two in class practice problems that align with the slides (good for interpreting tables) and/or A group of 9 slides starting around slide 29 that you can cut up and give to students for group practice constructing tables

Two Way Frequency Tables

Warm Up: Trig Review 𝟏. 3. John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33˚. How tall is the tree? 𝟐.

Warm Up: Trig Review cos 47.2 = 3 𝑥 𝑥∗ cos 47.2 =3 𝑥= 3 cos⁡(47.2) SOH-CAH-TOA Warm Up: Trig Review 𝟏. cos 47.2 = 3 𝑥 𝑥∗ cos 47.2 =3 𝑥= 3 cos⁡(47.2) 𝑥=4.4 cos 𝜃 = 7 10 θ= cos −1 ( 7 10 ) 𝑥=45.6˚ Adjacent Hypotenuse 𝟐.

SOH-CAH-TOA Warm Up: Trig Review 3. John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33˚. How tall is the tree? 𝟑𝟑˚ 𝟏𝟎𝟎 𝐟𝐞𝐞𝐭 tan 33 = ℎ 100 100∗ tan 33 =ℎ ℎ=64.94 feet

Two Way Frequency Tables Objective DOL SWBAT construct and analyze two-way tables. Given 2 CR problems, SW construct and analyze two-way tables with 80% accuracy. EQ: How can we represent information?

What’s the best kind of cake? Let them eat cake _________________ What’s the best kind of cake? Everything else Record the number that choose the dominant flavor and track of each student that chooses the dominate flavor. You may have them come to the board to initial which they prefer.

What’s better: Cake or cupcakes? Let them eat cake _________________ What’s better: Cake or cupcakes? Everything else Record the preference of every student. You may have them come to the board to initial their preference. Cake Cupcakes

Two Way Frequency Tables _________________ Everything else Complete the table based on our data. Cake Cupcakes Total Everything else Begin by adding the favorite flavor Cake Cupcakes

Two Way Frequency Tables Two way frequency tables: Show data in a way that lets us make comparisons For example… Cake Cupcakes Total Everything else How many students preferred our most popular flavor? How many students preferred cupcakes? If we’re just making dessert for the students who preferred our most popular flavor, should we make cake or cupcakes?

Two Way Frequency Tables Two way frequency tables: Show data in a way that lets us make comparisons For example… Cake Cupcakes Total Everything else Of the four options, what was the most common preference? Was there a relationship between the flavor we preferred and whether we prefer cake or cupcakes?

Example: Rainy Day Fun The Summer Camp for Kids staff is planning an indoor activity for the campers to do on rainy days. They are considering a Lego activity and a finger painting activity. They sent out a survey to all the kids who will be coming to the camp to find out their preferences.

Rainy Day Fun The staff organized the results of the survey into this table Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓

(the raw data for each combination) Notes Two way frequency tables: Show data in a way that lets us make comparisons 1st variable (type of cake) Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓 2nd variable (cake flavor) } } Joint Frequencies (the raw data for each combination) Marginal Frequencies (the totals)

Rainy Day Fun Seeing the results How many boys preferred Legos? Think-Write-Share Seeing the results How many boys preferred Legos? How many girls preferred Legos? How many campers preferred painting? How many girls responded to the survey? How many campers responded to the survey? Fist to Five Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓

Write your response on your whiteboard. Rainy Day Fun What’s wrong with this interpretation? More boys prefer Legos (37 to 26) More girls prefer painting (14 to 8) Therefore, they should let boys to Legos and girls paint Write your response on your whiteboard. Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓

Write your response on your whiteboard. Rainy Day Fun What’s wrong with this interpretation? More boys prefer Legos (37 to 26) More girls prefer painting (14 to 8) Therefore, they should let boys to Legos and girls paint Write your response on your whiteboard. Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓

Finding Missing Information

Key Club Fundraising The Key Club will sell candy as a fundraiser. They surveyed 80 students about their favorite candy. The results are shown in the frequency table. Fill in the missing information. Hint: The joint frequencies always add up to the marginal frequencies (37+43=80 and 19+18=37) Lollipop Peanut Butter Cup Total Boys 𝟏𝟗 Girls 𝟒𝟑 𝟑𝟓 𝟏𝟖 𝟑𝟕 𝟖𝟎 First, what do you know about the grand total? Whiteboards: Cell by cell

Hint: The joint frequencies always add up to the marginal frequencies Key Club Fundraising The Key Club will sell candy as a fundraiser. They surveyed 80 students about their favorite candy. The results are shown in the frequency table. Fill in the missing information. Hint: The joint frequencies always add up to the marginal frequencies (37+43=80 and 19+18=37) Lollipop Peanut Butter Cup Total Boys 𝟏𝟗 𝟏𝟖 𝟑𝟕 Girls 𝟐𝟔 𝟏𝟕 𝟒𝟑 𝟒𝟓 𝟑𝟓 𝟖𝟎

Two Way Relative Frequency Tables Back to summer camp

Two Way Relative Frequency Tables With one change to the table, we can make it easy to see what proportion of respondents preferred each option. Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓 Two Way Frequency Table (raw data) Legos Painting Total Boys 𝟎.𝟒𝟒 𝟎.𝟎𝟗 𝟎.𝟓𝟑 Girls 𝟎.𝟑𝟏 𝟎.𝟏𝟔 𝟎.𝟒𝟕 𝟎.𝟕𝟒 𝟎.𝟐𝟔 𝟏.𝟎𝟎 Two Way Relative Frequency Table (proportions)

Notes: Two Way Relative Frequency Tables Two way relative frequency table: A type of table that shows relative data in a way that lets us make proportional comparisons Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓 Two Way Frequency Table (raw data) Instead of total numbers, this shows the proportion of respondents with that preference. For example, only 16% of respondents were girls who prefer painting to Legos. Legos Painting Total Boys 𝟎.𝟒𝟒 𝟎.𝟎𝟗 𝟎.𝟓𝟑 Girls 𝟎.𝟑𝟏 𝟎.𝟏𝟔 𝟎.𝟒𝟕 𝟎.𝟕𝟒 𝟎.𝟐𝟔 𝟏.𝟎𝟎 Two Way Relative Frequency Table (proportions)

Notes: Two Way Relative Frequency Tables To make two way relative frequency tables… Divide the number in that cell by the total number of respondents Legos Painting Total Boys 𝟑𝟕 𝟖 𝟒𝟓 Girls 𝟐𝟔 𝟏𝟒 𝟒𝟎 𝟔𝟑 𝟐𝟐 𝟖𝟓 Two Way Frequency Table (raw data) Legos Painting Total Boys 𝟎.𝟒𝟒 𝟎.𝟎𝟗 𝟎.𝟓𝟑 Girls 𝟎.𝟑𝟏 𝟎.𝟏𝟔 𝟎.𝟒𝟕 𝟎.𝟕𝟒 𝟎.𝟐𝟔 𝟏.𝟎𝟎 Two Way Relative Frequency Table (proportions) 𝟑𝟕/𝟖𝟓 𝟖/𝟖𝟓 𝟒𝟓/𝟖𝟓 The grand total cell will always be 1.00. 𝟐𝟔/𝟖𝟓 𝟏𝟒/𝟖𝟓 𝟒𝟎/𝟖𝟓 𝟔𝟑/𝟖𝟓 𝟐𝟐/𝟖𝟓 𝟖𝟓/𝟖𝟓

Whiteboards: Cell by cell Key Club Fundraising In your notes for the Key Club Fundraiser, draw a relative frequency table next to the frequency table you already have. The first value is given to you below. Finish the first row, then move to the second. Lollipop Peanut Butter Cup Total Boys 𝟏𝟗 𝟏𝟖 𝟑𝟕 Girls 𝟐𝟔 𝟏𝟕 𝟒𝟑 𝟒𝟓 𝟑𝟓 𝟖𝟎 Two Way Frequency Table (raw data) Lollipop Peanut Butter Cup Total Boys 𝟎.𝟐𝟒 𝟎.𝟐𝟑 𝟎.𝟒𝟔 Girls 𝟎.𝟑𝟑 𝟎.𝟐𝟏 𝟎.𝟓𝟒 𝟎.𝟓𝟔 𝟎.𝟒𝟒 𝟏.𝟎𝟎 Two Way Relative Frequency Table (proportions)

Constructing Tables

Chocolates and Caramels Lena has a box of 18 chocolate and caramel candies. 10 candies have chocolate and caramel 3 candies have neither chocolate nor caramel 12 candies have chocolate Complete the table given this information. Caramel No caramel Total Chocolate 𝟏𝟎 𝟐 𝟏𝟐 No chocolate 𝟑 𝟔 𝟏𝟑 𝟗 𝟏𝟖 Step 1. Make a table Step 2. Fill in the given values Step 3. Calculate the missing values

Teacher Note You can print the next 9 slides in a 3 by 3 grid, cut them into rows and distribute them to students to work in groups. You could also give only one piece of information (rather than 3) to each student and then require them to find others with the same topic to gather enough information to complete the tables. Note: I’ve given no answers to the questions. Students will be responsible for giving the answers to the class.

Soccer vs. Football ESPN surveyed 50 respondents from the United States and Mexico about whether they prefer soccer or football. 26 people from the United States responded 8 people from the United States preferred soccer 23 people from Mexico preferred soccer Given this information, complete the two way frequency table and the two way relative frequency table. Step 1. Make a table Step 2. Fill in the given values Step 3. Calculate the missing values

Soccer vs. Football Soccer Football Total USA 𝟖 𝟏𝟖 𝟐𝟔 Mexico 𝟐𝟑 𝟏 𝟐𝟒 𝟑𝟏 𝟏𝟗 𝟓𝟎

Soccer vs. Football How many people from Mexico responded? Were both countries evenly represented? Why? What does the number 18 represent? Which sport is more popular overall? What patterns do you see in the data? What percent of U.S. respondents prefer soccer? What is the meaning of each marginal frequency?

Cats and Dogs A new Wal-Mart surveyed 75 people in the neighborhood about their pets. 25 people have a dog 20 people have a cat 9 people have a cat and a dog Given this information, complete the two way frequency table and the two way relative frequency table. Step 1. Make a table Step 2. Fill in the given values Step 3. Calculate the missing values

Cats and Dogs Dog No dog Total Cat 𝟗 𝟏𝟏 𝟐𝟎 No cat 𝟏𝟔 𝟑𝟗 𝟓𝟓 𝟐𝟓 𝟓𝟎 𝟕𝟓

Cats and Dogs How many respondents have no dog? What percent of respondents have no pet? How common is it to have a cat and dog? What does the number 55 represent? Which animal is more popular? Why? What patterns do you see in the data?

Ribs vs. Tacos Two food trucks work an event with 100 people. 40 people ate at the rib truck 50 people skipped the taco truck 35 people ate at neither truck Given this information, complete the two way frequency table and the two way relative frequency table. Step 1. Make a table Step 2. Fill in the given values Step 3. Calculate the missing values

Ribs vs. Tacos Ribs No Ribs Total Tacos 𝟐𝟓 𝟓𝟎 No tacos 𝟏𝟓 𝟑𝟓 𝟒𝟎 𝟔𝟎 𝟏𝟎𝟎

Ribs vs. Tacos Looking at all four joint frequencies, what was the most popular option? What was the second most popular option? What does the number 15 represent? What percent of people had no ribs? What do the marginal frequencies represent? What patterns do you see in the data?

Practice

Key Club Fundraising How many students preferred lollipops? WB checks How many students preferred lollipops? How many girls preferred peanut butter cups? How many boys answered the survey? Were boys and girls both evenly represented? Why? 45 17 37 Boys and girls were represented fairly evenly because about the same number of boys and girls responded. Lollipop Peanut Butter Cup Total Boys 𝟏𝟗 𝟏𝟖 𝟑𝟕 Girls 𝟐𝟔 𝟏𝟕 𝟒𝟑 𝟒𝟓 𝟑𝟓 𝟖𝟎

Key Club Fundraising Explain what the number 19 means in this table. WB checks Explain what the number 19 means in this table. Explain what the number 35 means in this table. 19 represents the number of boys who preferred lollipops. 35 represents the total number of people who preferred peanut butter cups. Lollipop Peanut Butter Cup Total Boys 𝟏𝟗 𝟏𝟖 𝟑𝟕 Girls 𝟐𝟔 𝟏𝟕 𝟒𝟑 𝟒𝟓 𝟑𝟓 𝟖𝟎

Key Club Fundraising What is the meaning of each marginal frequency? WB checks What is the meaning of each marginal frequency? What is the meaning of each joint frequency? The right column represents the total number of boys and girls who responded while the bottom row represents the total number of respondents who prefer each candy. Each joint frequency represents the preference for each candy of boys or girls. Lollipop Peanut Butter Cup Total Boys 𝟏𝟗 𝟏𝟖 𝟑𝟕 Girls 𝟐𝟔 𝟏𝟕 𝟒𝟑 𝟒𝟓 𝟑𝟓 𝟖𝟎

Practice: What’s for lunch? WB checks A total of 247 students were surveyed about what they liked best for lunch. The results can be shown in a two-way frequency table. Fill in the table. Begin with the grand total, then total juniors, then freshmen pizza. Pizza Salad Chicken Sandwich Total Freshmen 𝟏𝟖 𝟑𝟗 𝟏𝟎𝟐 Sophomores 𝟒𝟐 𝟖𝟕 Juniors 𝟐𝟖 𝟖𝟓 𝟔𝟓 𝟒𝟓 𝟓𝟖 𝟐𝟒𝟕

Practice: What’s for lunch? WB checks How many juniors preferred pizza? What was preferred by most freshmen? What was preferred least by sophomores? Overall, what was the most popular choice? 14 Pizza Salad Chicken sandwich Pizza Salad Chicken Sandwich Total Freshmen 𝟒𝟓 𝟏𝟖 𝟑𝟗 𝟏𝟎𝟐 Sophomores 𝟐𝟔 𝟏𝟗 𝟒𝟐 𝟖𝟕 Juniors 𝟏𝟒 𝟐𝟖 𝟏𝟔 𝟓𝟖 𝟖𝟓 𝟔𝟓 𝟗𝟕 𝟐𝟒𝟕

Practice: What’s for lunch? WB checks Were the different grade levels equally represented? What was the meaning of the number 28 in the table? No, there were 100 freshman and only 58 juniors. 28 juniors preferred chicken sandwiches. Pizza Chicken Sandwich Salad Total Freshmen 𝟒𝟓 𝟏𝟖 𝟑𝟗 𝟏𝟎𝟐 Sophomores 𝟐𝟔 𝟏𝟗 𝟒𝟐 𝟖𝟕 Juniors 𝟏𝟒 𝟐𝟖 𝟏𝟔 𝟓𝟖 𝟖𝟓 𝟔𝟓 𝟗𝟕 𝟐𝟒𝟕

Practice: What’s for lunch? WB checks What is the meaning of the number 85 in the table? Explain the meaning of the marginal frequencies in this table. A total of 85 students across all grades preferred pizza. The marginal frequencies (totals) on the right represent the number of respondents per grade and the ones on the bottom represent the total number of students with that preference. Pizza Chicken Sandwich Salad Total Freshmen 𝟒𝟓 𝟏𝟖 𝟑𝟗 𝟏𝟎𝟐 Sophomores 𝟐𝟔 𝟏𝟗 𝟒𝟐 𝟖𝟕 Juniors 𝟏𝟒 𝟐𝟖 𝟏𝟔 𝟓𝟖 𝟖𝟓 𝟔𝟓 𝟗𝟕 𝟐𝟒𝟕

Practice: What’s for lunch? WB checks Explain the meaning of the joint frequencies in this table How can you check your work to be sure you have filled in the table correctly? The joint frequencies represent how many students in each grade preferred each lunch option. Make sure the totals add up in each row and column. Pizza Chicken Sandwich Salad Total Freshmen 𝟒𝟓 𝟏𝟖 𝟑𝟗 𝟏𝟎𝟐 Sophomores 𝟐𝟔 𝟏𝟗 𝟒𝟐 𝟖𝟕 Juniors 𝟏𝟒 𝟐𝟖 𝟏𝟔 𝟓𝟖 𝟖𝟓 𝟔𝟓 𝟗𝟕 𝟐𝟒𝟕

Practice: What’s for lunch? WB checks Make a two way relative frequency table of the data Pizza Chicken Sandwich Salad Total Freshmen 𝟎.𝟏𝟖 𝟎.𝟎𝟕 𝟎.𝟏𝟔 𝟎.𝟒𝟏 Sophomores 𝟎.𝟏𝟏 𝟎.𝟎𝟖 𝟎.𝟏𝟕 𝟎.𝟑𝟓 Juniors 𝟎.𝟎𝟔 𝟎.𝟐𝟑 𝟎.𝟑𝟒 𝟎.𝟐𝟔 𝟎.𝟑𝟗 𝟏.𝟎𝟎

How can we represent information? Summary How can we represent information?

DOL A total of 176 people were surveyed about what outdoor fitness activity they preferred to do in the summer. The results can be shown in a two-way frequency table. Complete the table and answer the questions. Which sports get more popular with age? What was most popular overall? What percent of people preferred it? Were the different age groups represented evenly? Why? What do the marginal frequencies tell us? Soccer Basketball Jogging Total Teenagers 𝟖 𝟏𝟔 𝟔𝟐 College age 𝟏𝟕 𝟓𝟕 Adults 𝟏𝟖 𝟕𝟖 𝟒𝟑

DOL Which sports get more popular with age? Basketball and jogging get more popular with age. What was most popular overall? What percent of people preferred it? Soccer is most popular overall. 44% of respondents prefer it. Soccer Basketball Jogging Total Teenagers 𝟑𝟖 𝟖 𝟏𝟔 𝟔𝟐 College age 𝟐𝟑 𝟏𝟕 𝟓𝟕 Adults 𝟏𝟖 𝟐𝟐 𝟕𝟖 𝟒𝟑 𝟓𝟓 𝟏𝟕𝟔

DOL Were the different age groups represented evenly? Why? The age groups were represented about evenly. College age and adult respondents had 57 each and teenagers were only 5 away. What do the marginal frequencies tell us? The right column shows the total number of respondents for each age and the bottom row shows the total number of preferences each sport received. Soccer Basketball Jogging Total Teenagers 𝟑𝟖 𝟖 𝟏𝟔 𝟔𝟐 College age 𝟐𝟑 𝟏𝟕 𝟓𝟕 Adults 𝟏𝟖 𝟐𝟐 𝟕𝟖 𝟒𝟑 𝟓𝟓 𝟏𝟕𝟔