Getting Started

This guide will walk you through everything you need to get started using sampling paddles from Inference Supply Company: what to purchase, how to set up your materials, and a ready-to-use classroom activity that demonstrates one of the most powerful ideas in statistics — how sample size affects sampling variability.

By the end of this activity, your students will have hands-on evidence that larger samples produce more consistent estimates of a population proportion, while smaller samples tend to bounce around much more.

What You'll Need to Purchase

The table below lists everything required to run the introductory activity described in this guide. Beads and bins are not included with any Sampling Paddle purchase and should be sourced separately (see our Beads page for more information).

Initial Setup

Before class, prepare two sampling bins with different known proportions of red beads. This is the foundation for the activity.

Prepare Bin A

Choose a proportion and mix accordingly. For example, to create a bin that is 40% red, count out 4,000 red beads and 6,000 brown beads and combine them in the first bin. The 100-bead paddle can help you quickly and accurately count out the beads! Stir or shake the bin thoroughly to mix.

Prepare Bin B

Set up the second bin with a different proportion. For example, 60% red. Use 6,000 red and 4,000 brown. Again, mix well. Having two distinct populations lets you run the activity twice, or lets you assign different groups of students to different bins so they can compare results later.

A Note on Proportions

You have full flexibility here. Choose any two proportions that are meaningfully different from one another. Values like 40/60 and 60/40 work well because the difference is large enough for students to notice in their sample results, but not so obvious that the activity feels trivial.

Your First Activity: Seeing Sampling Variability

Overview

In this activity, students take repeated random samples from one bin using each of the three paddle sizes. They record the proportion of red beads in each sample, then plot all results on a dot plot. The key takeaway: the distribution of sample proportions is much more spread out when the sample size is small, and much more tightly clustered around the true proportion when the sample size is large.

Learning Goals

• Experience random sampling firsthand and observe natural sample-to-sample variation.
• Discover that larger samples produce estimates that are less variable (more precise).
• Build intuition for sampling distributions before encountering the concept formally.

Step-by-Step Instructions

Step 1: Introduce the Setup

Show students the bin (use Bin A to start) and explain that it contains thousands of red and brown beads mixed together in some unknown proportion. Their job is to use the sampling paddles to estimate the proportion of the bin that is red.

Important: Do not reveal the true proportion. Students should understand that in real statistical work, the population parameter is unknown — that’s why we sample.

Step 2: Demonstrate How to Use a Paddle

1.     Dip the paddle into the bin so that beads fill all the holes.

2.     Gently shake off excess beads so that exactly one bead sits in each hole.

3.     Lift the paddle out and count the number of red beads.

4.     Record the proportion: (number of red beads) ÷ (total holes in the paddle).

5.     Return all beads to the bin, stir, and repeat.

Step 3: Collect Samples with All Three Paddle Sizes

Have students (individually or in small groups) collect multiple samples with each paddle. We recommend at least 50 samples per paddle size to build a clear picture. Students should record their sample proportions individually or in their group, and will combine them with the class data to build a communal dot plot.

Step 4: Create Dot Plots

Once data collection is complete, have students create three dot plots — one for each paddle size — stacked vertically on the same number line so they can be compared directly. The horizontal axis should show the sample proportion of red beads (from 0.0 to 1.0), and each dot represents one sample.

For example, if a student drew 3 red beads out of 10 on the small paddle, they would place a dot at 0.30 on the small-paddle dot plot.

If you are working as a whole class, have each student come up and place a dot (or sticky note) on a shared whiteboard or poster. The class-wide dot plots will be richer and more convincing than individual ones.

Step 5: Discuss What You See

Guide a class discussion around the three dot plots. Here are some questions to prompt student thinking:

• "Which dot plot has the most spread? Which has the least?" Students should see that the small paddle (n = 10) produces the widest spread, while the large paddle (n = 100) clusters tightly.
• "Where is each distribution centered?" All three should be centered near the same value — the true population proportion — even though they have very different spreads.
• "If you had to guess the true proportion of red beads using just one sample, which paddle would you trust the most? Why?" This connects variability to the reliability of an estimate.
• "Did anyone get a sample proportion from the small paddle that was very far from the center? Could that happen with the large paddle?" Extreme results are common with small samples and rare with large ones.

Key Takeaway

Larger samples produce sample proportions that are less variable — they cluster more tightly around the true population proportion. Smaller samples are more “noisy” and can give estimates that are quite far from the truth. This is why sample size matters in statistics.

Going Further

Once students have completed this introductory activity, here are ways to extend the learning:

• Use Bin B. Repeat the activity with the second bin (which has a different proportion). Students can compare dot plots across bins and across paddle sizes, reinforcing that the spread depends on sample size, not on the true proportion.
• Predict before sampling. Before switching to a new paddle size, ask students to sketch what they think the dot plot will look like. Then sample and compare their prediction to the actual result.
• Connect to confidence intervals. After students have built intuition about variability, introduce the idea that a confidence interval is a formal way of capturing “how spread out” our estimate might be — and that wider intervals come from smaller samples.
• Explore bias vs. variability. Ask: “Are all three paddle sizes giving us good estimates on average, even though some are more variable?” This opens the door to discussing the difference between accuracy (bias) and precision (variability).
  

Practical Tips

• Stir between samples. Remind students to return beads to the bin and stir after every sample. This keeps each sample independent.
• Use proportions, not counts. Recording proportions (not raw counts) makes it possible to compare results across paddle sizes on the same dot plot axis.
• More samples = better dot plots. Fifty samples per paddle is a good minimum, but one hundred or more will produce even clearer patterns. In a full class, you may be able to collect 100+ samples quickly by having each student contribute four or five.
• Label everything. Make sure dot plots are clearly labeled with the paddle size and the axis scale. Students should be able to look at the three plots side by side and immediately see the difference.