Understand representative samples  Be US Census Bureau’s Chief Analyst (Lesson 2 of 5)  68
Student Objective
Students will be able to:
1. identify the conditions required to make a data sample a viable research strategy to credibly make inferences about a larger population
Instructions
Materials Required:
 Google Drive Account per student and for teacher
 Google Sheets familiarity within students
 Google Slides setup (described further below)
 US Census Bureau’s American Community Survey Data for 5 StatesTeacher Only (cleaned and available here)
 US Census Bureau’s American Community Survey Data for 5 StatesStudent Only (cleaned and available here)
 American Community Survey Data for New York OnlyTeacher Only (cleaned and available here)
 American Community Survey Data for New York OnlyStudents Only (cleaned and available here)
 Fake DataStudents Only (cleaned and available here)
 ACS Community Survey Data Codebook (cleaned and available here)
 Each student will each require a computer for this activity
Key Terms that will be Used:
 US Census Bureau
 American Community Survey (ACS)
 Household Income
 Food Stamp Recipients
 Codebook
 Variables
 Household Unit
 Numerical and Categorical Data
 Population
 Observations (new)
Step 1: Students Brainstorm the best way to “sample” a ton of meat
Using a digital board, have students provide at least 2 different ways to “sample” a create ton of burger meat

 Say:
 Say you work for the Food and Drug Administration in the government, and you are in charge of making sure that the meat everyone in the country eats is clean and safe!
 But, you can’t test EVERY single crate and piece of meat, so what do you think you should do?
 Write out at least 2 different ways to check a ton crate of meat without testing the entire crate and why you would be able to tell if the meat is safe or not.
 ThinkPairShare:
 Have 23 students share what their partner thought would be a good idea and why.
 Push their thinking:
 What if you had 100 crates?
 What about the meat at the bottom of the crate?
 Do you sample every crate in the same spot?
 Stamp:
 So, we can test a piece of the meat in the crate.
 And it’s unclear how to determine where we grab that piece of meat from.
 Introduce Today:
 So today, we’re going to learn how researchers and analysts solve this problem.
 Say:
Step 2: Connect Meat Sampling with Sampling a Data
Say and do:

 Introduce and define the idea of sampling from a population
 Definitions:
 Define sampling > fraction or percentage of a group
 Define population > a whole set of an entire group, includes EVERY member in the group
 Define observations > the unit of data under observation
 a sample is made up of some of the observations possible
 a population is made up of all the observations possible
 “a row” within our data
 “Analysts and researchers usually can’t test an entire population, so they test a sample of the population that represents the population. This is called a “representative sample! So how do we make a representative sample?”
 Definitions:
 Introduce and define the idea of sampling from a population
Step 3: Introduction to New Material – Introduce the Enduring Question and Goal of Activity
Now, we’re going to ask:
 Under what conditions does a sample represent an entire population?
Step 4: Set the stage for students to work within Google Sheets with Filtering and Pivot Tables
[Teacher To Do’s Beforehand:]
 Make a copy of “NewYorkDataOnly_TeacherOnly” for self reference
 Make a copy of “FiveStatesOfData_TeacherOnly”
 Make a copy of “NewYorkDataOnly_Students”
 Each student will make a copy of your copy and label it, “StudentFullName_NewYorkOnly_Students” and share it with you
 Make a copy of “FiveStatesOfData_Students”
 Each student will make a copy of your copy and label it, “StudentFullName_FiveStatesOfData_Students” and share it with you
 Make a copy of “FakeData_Students”
 each student will make a copy of your copy and label it, “StudentFullName_FakeData_Students” (does not need to be shared)
Set students up for success through MiniLessons:
 How to filter data in Google Sheets using “FakeData_Students”
 Click in cell A1 in Google Sheet with data
 Move cursor to Toolbar –> Click Funnel Icon [look to the right for funnel icon]
 Click on upside down green triangle for a variable and select only the entries you want
 EX: I want only New York in 2010
 YEAR –> 2010
 StateName –> New York
 EX: I want only New York in 2010
 Model for students, then allow them to do it with practice:
 “Filter for Nebraska, 2019”
 “Filter for Wisconsin, 2010”
 How to calculate statistics (averages) in Google Sheets using “FakeData_Students”
 Model for students how to filter and have them do it with you:
 Have students filter data to get only: New York in 2019
 Have them copy/paste that data into a new tab, “NewYork2019”
 [Within “NewYork2019” Tab] Select all the data
 Toolbar –> Data –> Pivot Table –> New Sheet –> Create
 Select Rows and Columns
 [In Pivot Table Editor] Rows –> Add –> “StateName” (New York)
 DeSelect “Show total”
 [In Pivot Table Editor] Values –> Add –> HHINCOME
 Click “Summarize by”
 Select “Average”
 [In Pivot Table Editor] Rows –> Add –> “StateName” (New York)
 Have students practice
 Find average household income for Nebraska in 2010
 Find average number of people in the household within Montana in 2019
 Have discussion on what the “AVERAGE” means for the variables “FOODSTMP” and “OWNERSHP”
 Answer: average of 1s and 0s is the percent value (show them the math)
 Practice:
 Percentage of households that received Food Stamps in Montana in 2019
 Percentage of households that owned their home in Nebraska in 2010
 Model for students how to filter and have them do it with you:
Step 5: Have students calculate sample statistics
 Share with students 2010 New York Data in a separate google sheet
 Have students make their own individual copy of the data and have them share it with you (the teacher)
NOTE: In this step, students should be calculating these statistics using Google Sheets Pivot Tables
 Create google slides with one slide allocated to each student, and each student has a table they will fill in for this activity
Sample Types  
Variable  Population  First 20  100 block  10% Random 
HHINCOME  
OWNERSHP  
NumInHouse  
FOODSTMP  
ROOMS  
PersRm 
Step 6: Have students calculate the population statistics
Students calculate the averages of each criteria variable for the Population, using all rows from the 2010 New York dataset

 Steps for students: (independent practice)
 select all data
 insert pivot
 calculate numbers
 Fill in table with calculated values
 Actual Population Data Calculations:
 Average Number of People in Household –> 2.49
 Percentage of Households Own Home –> 62.09%
 Average Household Income–> 80,186.07
 Percentage of Households Receiving Food Stamps –> 12.46%
 Average Number of Rooms –> 5.76
 Average Persons per Room –> 0.4
 Steps for students: (independent practice)
Step 7: Have students calculate statistics using a sample of the first 20 rows (or observations) of the data
Students calculate the averages of each criteria variable, using only the first 20 observations (or rows, or people) of the 2010 New York data

 Steps for students: (independent practice)
 Select first 20 observations
 copy/paste into new tab
 select data in new tab
 insert pivot
 calculate numbers
 Fill in table with calculated values
 Actual Data Results
 Average Number of People in Household –> 2.9
 Percentage of Households Own Home –> 50%
 Average Household Income–> $156, 805.00
 Percentage of Households Receiving Food Stamps –> 20%
 Average Number of Rooms –> 6.55
 Average Persons per Room –> 0.47
 Steps for students: (independent practice)
Step 8: Have students calculate statistics using a sample of any 100 contiguous rows (or observations) of the data
Students calculate the averages of each criteria variable, using any contiguous 100 rows of the 2010 New York data

 Steps for students: (independent practice)
 Select 100 observations as one big block
 copy/paste into tab
 select data in tab
 insert pivot
 calculate numbers
 Fill in table with calculated values
 Actual Data Results
 Average Number of People in Household –> [will vary]
 Percentage of Households Own Home –> [will vary]
 Average Household Income–> [will vary]
 Percentage of Households Receiving Food Stamps –> [will vary]
 Average Number of Rooms –> [will vary]
 Average Persons per Room –> [will vary]
 Steps for students: (independent practice)
Step 9: Have students calculate statistics using a 10% Random Sample of the data
Share and inform students:
 Define 10% Random Sample:
 10% –> 10% of the population (one tenth)
 Random –> selections that have the same probability of being selected (think of lottery balls, each ball has an equal chance of being chosen)
Students calculate the averages of each criteria variable, using the 10%RandomSample data (preprepared for students in NewYorkDataOnly_Students


 Actual Values
 Average Number of People in Household –> 2.42
 Percentage of Households Own Home –> 61.08
 Average Household Income–> $81, 432
 Percentage of Households Receiving Food Stamps –> 12.03%
 Average Number of Rooms –> 5.71
 Average Persons per Room –> 2.42
 Actual Values

Step 10: ThinkPairShare — Students Compare Each Sample’s Statistics with the Population Statistics
 Think – 4 minutes
 Using your filled out table of statistics by sample, which sample best represents the population?
 How do you know?
 Why not the other samples?
 Pair – 2 minutes
 Share with your partner what sample you selected as representative and why.
 Share – 2 minutes
 Select 23 students to share out
 Exemplar Response:
 The sample that best represents the population is the 10% Random Sample because the statistics are almost the same. The other samples’ statistics might have one or two variables that are close but the others are very different.”
 Exemplar Response:
 Select 23 students to share out
 PUSH THINKING
 What are the 2 conditions required for a sample to be representative of the population?
 Hint: look at the title of the best sample we chose
 Exemplar answer:
 The sample must be:
 random
 10% of the population
 The sample must be:
 What are the 2 conditions required for a sample to be representative of the population?
Step 11: Stamp and End Lesson, Preview Next Lesson:
 Stamp
 Today we asked the question: “Under what conditions does a sample represent an entire population?”
 We answered with:
 “A sample is representative when it is 10% of the population and is random.”
 Preview Next Lesson:
 Next lesson, you will actually conduct a 10% random sample so you can run your analysis for your selected state as the US Census Bureau Chief Analyst!”
Google Slides Setup Instructions:
 Each student should have 3 slides assigned to them
Slide 1: Variable Names and Descriptions
What are the variables available in the American Community Survey of 5 states?  
Variable Name  Descriptions
(in your own words) 
Data Type
(numerical or categorical) 
Slide 2: Students select the variables they want to use for analysis
Select 3 or 4 variables for your research and analysis  
Variable  Reason Selected 
What were the variables you chose NOT to use for analysis?  
Why did you not choose the other available variables?  
Slide 3: Variables Chosen and Values by Time Period
What state will you write a report on? ________________ 

Variables

Time Period 1:
Beginning Year: _________ 
Time Period 2
End Year: _________ 
1.  
2.  
3.  
4. 