# Conduct a representative sample | Be US Census Bureau’s Chief Analyst (Lesson 3 of 5) | 6-8 ### Student Objective

Students will be able to:
1. Conduct a representative, random sample and compare it to the population, using a simulation in google sheets.

### Instructions

Materials Needed:

### Step 1:  Own It Activity

• Think-Pair-Share: Ask students, “How would you conduct a representative sample of 100 one-ton-crates of meat?”

### Step 2:  Introduce Enduring Question

• Last lesson, we asked ourselves, “What conditions are required for a sample to representative of its population?”
• Today, we ask, “How do we conduct a 10% random sample from a population using Google Sheets?

### Step 3: Model How to Randomly Select Observations in Dataset

• Model for students, as they do it with you:
• Open up, “FakeData_Students”
• In the tab, “Sheet1,” click the cell under the words, “Random Students” in column K
• Check to make sure you can see the following google code in the cell:
• =ArrayFormula(Array_Constrain(vlookup(Query({ROW(A1:A101),randbetween(row(A1:A101)^0,9^9)},“Select Col1 order by Col2 Asc”),{row(A1:A101),A1:A101},2,FALSE),100*0.1,1))
• Double click into the cell, highlight the entire google code, and copy it by pressing “CTRL+C”
• Click out of the cell
• Click back on the cell
• Press “CTRL+V” to paste
• The numbers should now have changed — these are the SERIAL numbers of households in our 10% random sample
• we have just run a random lottery, where we grabbed 10% of lottery balls, but in this case they are households
• Explain to students:
• Each time you press “CTRL + C” into that cell, you re-run the randomization (or the lottery)
• “You’ve now conducted a 10% random sample, but you only have the SERIAL identifier of each household.  We have to make sure we get the household data that comes with the households themselves.”
• Have students:
• Look at tab, “10%RandomSample” and you’ll see that the SERIAL numbers sample are connected to the household data!”
• Test and try out:
• have students run a new sample
• check the “10%RandomSample” tab to see if the SERIAL numbers match with their data

### Step 4: Have Students Conduct a Random Sample

• Have students open up, “NewYorkDataOnly_Students”
• Have students conduct a random sample on their NewYorkDataOnly_Students on their own

NOTE:

• The sample will take a 5-7 minutes to finish and calculate.
• Use the extra time to teach students how the function works for conducting a random sample
• =ArrayFormula(Array_Constrain(vlookup(Query({ROW(A1:A101),randbetween(row(A1:A101)^0,9^9)},“Select Col1 order by Col2 Asc”),{row(A1:A101),A1:A101},2,FALSE),100*0.1,1))
• Sections of function:
• ROW(A1:A101) –> A1:A101 means the cells where my SERIAL numbers are
• 100*0.1 –> a calculation for the number of observations I want to sample.  100 = all observations in data; 0.1 = 10%; 100*0.1 = 10% of 100 observations (total of 10)

### Step 5: Have Students Calculate Statistics from Their Random Sample and Compare to Population Statistics

• Using Google Sheets Pivot Tables, have students calculate the average value of each variable for:
• their random sample
• their total NY 2010 population
• Think-Pair-Share:
• Have students compare their population statistics with their sample statistics
• Are they the same?
• Are they different?  How different?
• Can you use this sample to represent the population?

### Step 6: Stamp and End Lesson, Introduce Next Topic

• In this lesson, we asked ourselves, “How do we conduct a representative 10% random sample?”
• Tomorrow, we will learn how to make statistical inferences from our sample statistics when we compare them to other population statistics from a different sample of the same information/