Teacher Note: What to print For this lesson, you can print: Homework Two in class practice problems...

Two Way Frequency Tables

Warm Up: Trig Review

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?

𝟏 .

𝟐 .


𝟏 .

𝟐 .

SOH-CAH-TOA

Adjacent

Hypotenuse


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?

𝟏𝟎𝟎 𝐟𝐞𝐞𝐭 𝟑𝟑 ˚

SOH-CAH-TOA

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?

Let them eat cake

What’s the best kind of cake?

_________________ Everything else

Let them eat cake

What’s better: Cake or cupcakes?


Cake Cupcakes



Cake Cupcakes

Cake Cupcakes

Total

Everything else

Total

Complete the table based on

our data.


Cake Cupcakes

Total

Everything else

Total

Two way frequency tables: Show data in a way that lets us make comparisons

For example…

• 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?


Cake Cupcakes

Total

Everything else

Total


For example…

• 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

Girls

Total

Notes



Boys

Girls

Total

1st variable(type of cake)

2nd variable

(cake flavor) } }

Marginal Frequencies(the totals)

Joint Frequencies(the raw data for each

combination)

Rainy Day Fun

Seeing the results1. How many boys preferred Legos?2. How many girls preferred Legos?3. How many campers preferred painting?4. How many girls responded to the survey?5. How many campers responded to the survey?


Boys

Girls

Total

Think-Write-Share

Fist to Five

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.


Boys

Girls

Total

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.

LollipopPeanut Butter

CupTotal

Boys

Girls

Total

Hint: The joint frequencies always add up to the marginal frequencies

and

𝟖𝟎

𝟑𝟕𝟏𝟖

First, what do you know about the grand

total?Whiteboards: Cell by cell


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.


CupTotal

Boys

Girls

Total

Hint: The joint frequencies always add up to the marginal frequencies

and

BACK TO SUMMER CAMP

Two Way Relative Frequency Tables

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.


Boys

Girls

Total

Two Way Frequency Table

(raw data)

Two Way Relative Frequency Table

(proportions)


Boys

Girls

Total

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


Boys

Girls

Total


(raw data)


(proportions)


Boys

Girls

Total

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.

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


Boys

Girls

Total


(raw data)


(proportions)


Boys

Girls

Total

The grand total cell will always be .

𝟑𝟕 /𝟖𝟓𝟐𝟔 /𝟖𝟓

𝟖/𝟖𝟓𝟏𝟒 /𝟖𝟓

𝟔𝟑 /𝟖𝟓 𝟐𝟐 /𝟖𝟓

𝟒𝟓 /𝟖𝟓𝟒𝟎 /𝟖𝟓𝟖𝟓 /𝟖𝟓


In your notes for the Key Club Fundraiser, draw a relative frequency table next to the frequency table you already have.


CupTotal

Boys

Girls

Total

The first value is given to you below. Finish the first row, then move to the second.


CupTotal

Boys

Girls

Total


(raw data)


(proportions)

Whiteboards: Cell by cell

Constructing Tables

Chocolates and Caramels

Lena has a box of 18 chocolate and caramel candies.10 candies have chocolate and caramel3 candies have neither chocolate nor caramel12 candies have chocolate

Complete the table given this information.

CaramelNo

caramel Total

Chocolate

No chocolate

Total

Step 1. Make a table

Step 2. Fill in the given values

Step 3. Calculate the missing values

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 responded8 people from the United States preferred

soccer23 people from Mexico preferred soccer

Given this information, complete the two way frequency table and the two way relative frequency

table.




Soccer vs. Football

Soccer Football Total

USA

Mexico

Total

Soccer vs. Football

1. How many people from Mexico responded?

2. Were both countries evenly represented? Why?

3. What does the number 18 represent?

4. Which sport is more popular overall?

5. What patterns do you see in the data?

6. What percent of U.S. respondents prefer soccer?

7. 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 dog20 people have a cat9 people have a cat and a dog


table.Step 1. Make a table



Cats and Dogs

Dog No dog Total

Cat

No cat

Total

Cats and Dogs

1. How many respondents have no dog?

2. What percent of respondents have no pet?

3. How common is it to have a cat and dog?


5. Which animal is more popular? Why?


Ribs vs. Tacos

Two food trucks work an event with 100 people.40 people ate at the rib truck50 people skipped the taco truck35 people ate at neither truck


table.




Ribs vs. Tacos

Ribs No Ribs Total

Tacos

No tacos

Total

Ribs vs. Tacos

1. Looking at all four joint frequencies, what was the most popular option?

2. What was the second most popular option?


4. What percent of people had no ribs?

5. What do the marginal frequencies represent?


Practice


1. How many students preferred lollipops?2. How many girls preferred peanut butter cups?3. How many boys answered the survey?4. Were boys and girls both evenly represented?

Why?


CupTotal

Boys

Girls

Total

45

17

37

Boys and girls were represented fairly evenly because about the same number of boys and girls responded.

WB checks


5. Explain what the number 19 means in this table.

6. Explain what the number 35 means in this table.


CupTotal

Boys

Girls

Total

19 represents the number of boys who preferred lollipops.

35 represents the total number of people who preferred peanut butter cups.

WB checks


7. What is the meaning of each marginal frequency?

8. What is the meaning of each joint frequency?


CupTotal

Boys

Girls

Total

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.

WB checks

Pizza SaladChicken

Sandwich Total

Freshmen

Sophomores

Juniors

Total

Practice: What’s for lunch?

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.

WB checks

𝟒𝟓

𝟐𝟒𝟕𝟓𝟖


1. How many juniors preferred pizza?2. What was preferred by most freshmen?3. What was preferred least by sophomores?4. Overall, what was the most popular choice?

Pizza SaladChicken

Sandwich Total

Freshmen

Sophomores

Juniors

Total

WB checks

14

Pizza

Salad

Chicken sandwich


5. Were the different grade levels equally represented?

6. What was the meaning of the number 28 in the table?

PizzaChicken

Sandwich Salad Total

Freshmen

Sophomores

Juniors

Total

WB checks

No, there were 100 freshman and only 58 juniors.

28 juniors preferred chicken sandwiches.


7. What is the meaning of the number 85 in the table?

8. Explain the meaning of the marginal frequencies in this table.

PizzaChicken


Freshmen

Sophomores

Juniors

Total

WB checks

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.


9. Explain the meaning of the joint frequencies in this table

10. How can you check your work to be sure you have filled in the table correctly?

PizzaChicken


Freshmen

Sophomores

Juniors

Total

WB checks

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.


11. Make a two way relative frequency table of the data

PizzaChicken


Freshmen

Sophomores

Juniors

Total

WB checks

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.1. Which sports get more popular with age?2. What was most popular overall? What percent of people

preferred it?3. Were the different age groups represented evenly? Why?4. What do the marginal frequencies tell us?Soccer

Basketball

Jogging Total

Teenagers

College age

Adults

Total

DOL

1. Which sports get more popular with age? Basketball and jogging get more popular with age.

2. What was most popular overall? What percent of people preferred it?

Soccer is most popular overall. 44% of respondents prefer it.

SoccerBasketbal

lJoggin

g Total

Teenagers

College age

Adults

Total

DOL

3. 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.

4. 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

College age

Adults

Total

Teacher Note: What to print For this lesson, you can print: Homework Two in class practice problems...

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