1.1.2 – Other Random Sampling Methods
There are many ways to randomly sample. Let’s review what we’ve already learned about, and
compare and contrast it to a few more methods.
The student council wants
to conduct a survey about
use of the school library
during the first five minutes
of an all-school assembly
in the auditorium. There
are 800 students present at
the assembly. Here is a
map of the auditorium.
Note that students are
seated by grade level and
that the seats are
numbered from 1 to 800.
1. Describe four different ways we could sample from this group.
Randomly select from among all students – simple random sample
Sample by row/grade level – stratified random sample
Sample by column – cluster sample
Sample as they enter – systematic random sample
2. Describe how to obtain a sample of 80 students using a simple random sampling.
Use a random number generator to generate 80 unique random values from 1 to 800 and
give the survey to the students in the corresponding seats.
3. Describe how to obtain a sample of 80 students using stratified random sampling. Explain
your choice of strata and why this method might be preferred to simple random sampling.
Stratify by grade level. For each grade, label the students from 1-200. Randomly generate 20
unique values from 1 to 200. Give the survey to those students. Repeat for each grade.
Stratification reduces variability and guarantees proportionate representation in the sample.
4. Describe how to obtain a sample of 80 students using cluster sampling. Explain your choice of
clusters and why this method might be preferred to simple random sampling.
Each column is a cluster. Label the columns from 1 to 20. Randomly generate 2 unique
values from 1 to 20. Give the survey to the 80 students sitting in those columns.
Cluster sampling is much more efficient than finding 80 seats scattered about the auditorium.
5. Describe how to obtain a sample of 80 students using systematic random sampling. Explain
why this method might be preferred to simple random sampling.
Sample every 10th student. Generate a random integer from 1 to 10, call this k. Select the kth
student to enter, and every 10th student after them.
Systematic sampling is much more efficient than SRS because the individuals come to you
instead of you going to them.
Big Ideas:
•
•
•
Stratified Random Sample – Group by
similar characteristics, SRS within each
group
Cluster Sample – Group by similar location,
SRS of clusters
Systematic Random Sample – Randomly
select in the first k, and every k after
Why use instead of SRS?
• Stratified
o Reduced variability
o Proportionate representation
• Cluster, Systematic
o More efficient
CHECK YOUR UNDERSTANDING
A factory runs 24 hours a day, producing 15,000 wood pencils per day over three 8-hour shifts—day,
evening, and overnight. In the last stage of manufacturing, the pencils are packaged in boxes of 10
pencils each. Each day a sample of 300 pencils is selected and inspected for quality.
1. Describe how to select a stratified random sample of 300 pencils. Explain your choice of strata.
Because the quality of the pencils might be the same within each of the shifts, but differ across the
shifts, use the shifts as strata. At the end of each 8-hour shift, label all the pencils produced during
that shift 1 to 5000, where N is the total number of pencils produced on that shift. Generate 100
different random integers from 1 to 5000 and select those pencils for inspection.
2. Describe how to select a cluster sample of 300 pencils. Explain your choice of clusters.
The boxes of 10 pencils could be used as a cluster sample because it would be relatively easy to
select boxes of 10 pencils. At the end of the day, label all the boxes of pencils 1 to 1500. Generate
30 different random integers from 1 to 1500 and inspect all the pencils in the selected boxes.
3. Describe how to select a systematic random sample of 300 pencils.
Select every 15,000/300 5 50th pencil that comes off the Start by randomly selecting a number from
1 to 50. Select that pencil and every 50th pencil thereafter until 300 pencils have been selected.
4. Explain a benefit of each of these three methods in this context.
Stratified: We are guaranteed to inspect 100 pencils from each of the three shifts.
Cluster: Simplifies the sampling process.
Systematic: It is easier to find the selected pencils by selecting them as they come off the
production line, which will guarantee that samples of pencils that were manufactured at regular
intervals over the course of the day are selected.