AP Statistics Sampling Designs- Random Rectangles
The Rectangles sheet has 100 random rectangles on it. They are already numbered so that you can easily sample them by randomly generating numbers. They are of varying size (area). Each box is 1 unit of area.
Example: 3 units 2 : 6 units 2 : 8 units 2 :
You will be doing 5 different TYPES of samples. Each time you will be sampling a total of 5 rectangles.
1. Judgmental Sample
Study the rectangles on the front side of the sheet (side #1). After studying the 100 rectangles, select ANY 5 that you believe are representative of the whole population.
Let Z be the size (area) of the rectangle. Write the rectangle # that you chose, and the size (area) of your 5 below, then find the mean size ( z )
Rectangle # z

Area (Z)
2. Simple Random Sample (SRS)
Using the calculator, generate 5 random numbers from 1 to 100 (use randInt(1, 100)). Find the matching rectangle and its size. Record the info below, then find the mean.
Rectangle # z

Area (Z)
3. Stratified Sample
On the back side of the rectangles, the rectangles have been separated into 5 groups (strata) based on size. Each strata now has 20 rectangles of similar size. We want to take a sample in each strata, then combine these to make our total sample.
Generate a random number between 1 and 20 (randInt(1,20)), and use that rectangle in Strata #1. Record the # you generated and rectangle size below. Then do the same thing for each of the other strata (generate a new random number between 1 & 20 each time). Record the sizes and find the mean.
Strata 5
Strata 1 Strata 2 Strata 3 Strata 4
Rectangle # z

Area (Z)

4. Cluster Sample
Here we want to take a sample of a group of rectangles that are near each other. We still want a sample of five rectangles total, and we also still want it to be a random sample.
Look back at the original sheet of rectangles (side #1). We can put the rectangles into clusters (groups) of five based on their assigned number. So the first cluster would be rectangles #1-5, the second cluster would be rectangles #6-10, and so on giving us 20 clusters to sample. r , between 1 and 20. This is the cluster you Let’s choose a cluster for our sample. To do this, choose a random number, will use for your sample. Now calculate 5r – 4 , and then 5r. The rectangles with numbers from 5r – 4 to 5r are your cluster.
This should be 5 rectangles.
Ex: You get the random number 6. 5(6) – 4 = 26 and 5(6) = 30. So this means you are looking at rectangles #26 – 30.
Record the 5 rectangle numbers below, then their size, then the mean.
Random Number r

Rectangle # z

Area (Z)
5. Systematic Sample
Use the original sheet of rectangles (side #1). Randomly generate a number between 1 and 20. This is the first rectangle you will sample. Write this rectangle # in the first box below. Add 20 to the random number to get the second rectangle you will sample. Continue to add 20 to get the next three rectangles for your sample. This is like having to sample every 20 th person who passes you.
Ex: You get the random number 6. Then you would inspect rectangles 6, 26, 46, 66, and 86.
Record the rectangle numbers, sizes, and then find the mean size.
Random Number r

Rectangle # z

Area (Z)
Record your means for each of the 5 methods on the board.
Using a partner to help split up the work, calculate the
means for each of the 5 methods.
Record them below:
Judgemental SRS Stratified Cluster Systematic
Average Class Area
The actual mean is 7.42. Which method was the closest to the correct mean?