Sampling Techniques – An Activity with Poker Chips

Advance Preparation:
Have a brief survey ready for sampled students to answer. I use three
questions, one giving categorical data, another giving discrete data,and the
third giving continuous data. This data can then be used for other examples.
Need two sets of matching chips. Number the chips from 1 to N, where N is
the class size. Decide on the mix of colors. (see stratified sample below).
Choose a sample size, n.
I purchase some candy to use as a reward.

Classroom Activity. The students in the class form the population of interest.
A. Volunteer sample: Ask for a few volunteers to answer a survey. After
answering the survey, reward the volunteers (ie with candy). The class
becomes involved and students hope to be selected.
B. Random Sample: From your bag of matching chips, select n. Since each chip
is numbered, you can announce color and number (or, you can use a
calculator to generate the random numbers). Have the students in the
random sample answer the same survey and give them the reward.
C. 1 in K Systematic Sample: Have students line up in numerical order in front of
the room. Choose k. From the first k students, chose 1 at random. (can use
your matching chips if sort them out ahead of time or can use calculator
random number function). Have that student step forward. Then have every
kth student step forward. The selected students will answer the survey and be
given a reward.
D. Stratified Sample: Have students group according to the color of the poker
chip. (the like characteristic is chip color). As poker chips come in three
colors, you will have three strata. Randomly sample from each strata, using
the matching chips. (As students are moving into groups, you can sort your
chips.) If you vary the size of the strata, you may draw different size samples
proportionately from each. Or, you may draw an equal sample from each
strata and find a weighted average. Once again, those sampled answer the
survey and are given a reward.
E. Cluster Sample: Have students group according to the color of the poker chip.
Each group is a mini-population. Randomly select one color. Give the survey
and reward to each student in that color group.
F. Multistage: Cluster followed by random sample.

Followup Activities
1. How many times were the individual students selected to answer the
survey? (As they took a piece of candy each time selected, they know.)
Discuss the fact that some are chosen frequently, others never. This
happens in the world as well (i.e. jury duty)
2. Look at survey results for each type of sample. As a minimum, a
frequency table can be created for the categorical variable. (I divide the
class into groups and give each group one set of completed surveys. The
results are summarized on the board.) The results will differ from one
sample to the other. Discuss the fact that statistics vary. As the groups
are working, I find the results for the entire population (the parameter).
Compare the parameter with the statistics. Reinforce that statistics vary
and the parameter is fixed.
3. Stress the difference between stratified sampling and cluster sampling.
This seems to be the most difficult distinction for the student to make.
Presented by Donna Gorton, Math Instructor, Butler County Community College
Volunteer Sample:
Please answer the following questions:
1. Are you male or female?
2. How many siblings do you have?
3. How far do you drive (one-way) to work?
Random Sample:
Please answer the following questions:
1. Are you male or female?
2. How many siblings do you have?
3. How far do you drive (one-way) to work?
Systematic Sample
Please answer the following questions:
1. Are you male or female?
2. How many siblings do you have?
3. How far do you drive (one-way) to work?
Stratified Sample:
Please answer the following questions:
1. Are you male or female?
2. How many siblings do you have?
3. How far do you drive (one-way) to work?
Cluster Sample:
Please answer the following questions:
1. Are you male or female?
2. How many siblings do you have?
3. How far do you drive (one-way) to work?
Multi-Stage Sample
Please answer the following questions:
1. Are you male or female?
2. How many siblings do you have?
3. How far do you drive (one-way) to work?