# Activities to Teach Students to Identify Representative, Random, and Biased Samples

As students progress through their school years, they begin to encounter more and more statistical concepts. One of the most important of these concepts is the idea of sampling. When dealing with a large data set, it is usually impossible to study every single individual or data point. Instead, one must select a smaller group, or sample, to study in order to draw conclusions about the larger population.

However, not all samples are created equal. Some may be representative of the population they are drawn from, some may be random, and others may be biased, meaning they do not accurately reflect the larger group. Therefore, it is crucial that students learn how to identify these different types of samples and understand why they are important. Here are a few activities that can be used to teach these concepts.

1. The M&M Experiment

For this activity, students will need a large bag of M&Ms and a record sheet to document their observations. Break the class into small groups and give each group a handful of M&Ms. Ask them to separate the candies by color and record the number of each color on their record sheet. Once this is complete, have them compare their results with another group and discuss any differences they notice.

From this activity, students can see that even though they are drawing from the same bag of M&Ms, their samples can differ greatly. This is much like different samples drawn from a population.

2. Sample Scavenger Hunt

In this activity, students will create scavenger hunt lists of items that can be found in their classroom or school. They should work in groups and each group should create two lists: one that is representative of the population (such as items found in a math class) and one that is biased (such as items found only in the teacher’s lounge). Once the lists are created, each group will give their biased list to another group, who will then have to identify which items on the list make it biased.

This activity teaches students to identify samples that are representative versus those that are biased, as well as methods for identifying the source of bias.

3. Random Picture Selection

For this activity, students will need access to a large number of pictures, either in print or online. Ask students to select a picture at random and then determine what population the picture represents. In addition, have them consider whether the picture is biased in any way.

This activity not only teaches students how to identify random samples, but also enables them to understand the difference between pictures that are representative and pictures that contain bias.

4. Sampling in the News

For this ongoing activity, teachers can give students the task of locating and analyzing news articles that involve sampling. Students should be asked to document the article, describe the population being studied, identify the type of sample used, and explain any bias that may be present.

This activity can be done throughout the year as new articles arise. It teaches students to look for sampling concepts in real-world situations and provides a way for them to see how the concepts they are learning in the classroom are applied in the real world.

In conclusion, sampling is an important statistical concept that students must understand in order to draw valid conclusions and make informed decisions. Utilizing activities that engage students through hands-on experiences and real-world situations can help students both understand and retain the material. With a strong understanding of sampling, students will be better equipped to navigate the world of statistics and make informed decisions throughout their lives.