In this activity, students learn that often the best we can do to select a representative sample is to avoid sampling methods that will be inherently biased one way or another. A randomly selected sample is not guaranteed to be representative of the population, but other methods are often biased and thus more likely to produce samples that are not representative of the population.

The purpose of the discussion is for students to understand that some methods of sampling are better than others. Although there may be no way to guarantee that a sample is representative of the population, we can certainly avoid methods that will definitely result in some groups being over- or under-represented.

Poll the class on which of the given methods is best for each situation. Record the answers for all to see.

Select several students to explain benefits and drawbacks of each of the sampling methods. After each method has been analyzed for a situation, ask if students have ideas for better ways to get a representative sample for the situation.

Ask students, “What are some important things to consider when getting a sample?” (Is there a group that this method will show preference for? Is there a group that will automatically be left out of my sample based on the method? If there are groups I didn’t even think about, does my method have a way of reaching them?)

Explain that people often have biases that may lead them to over- or under-represent some groups in their samples, whether the biases are obvious or not. For example, to find which candidate might be leading in a political race, we might try calling people to survey their preference. This could make our sample biased towards people who are willing to answer their phones when an unknown number calls. Due to (sometimes hidden) biases, the best method for selecting samples is to remove as much of the personal selection as possible.

In this activity, students see an example of a hidden bias. Although the method of selecting straws by taking out the first one touched in the bag appears fair and random, it produces samples that are not representative of the population (MP1). In the next activity, students explore ways to resolve the problem by finding other methods of selecting a sample that would be fair for this same context.

Ask students:

• “What does it mean for a process of selecting straws to be ‘fair’?” (There should be an equal chance for each item to be selected.)
• “Is this selection process fair?” (No, the shorter pieces probably fell to the bottom of the bag and are less likely to be touched first.)

Reveal the contents of the bag.

• “Are your samples representative of the contents of the bag? Explain your reasoning.” (No, there are a lot more longer straws in our samples than in the bag.)
• “Does every straw in the bag have an equal chance of being selected?” (Longer straws are probably touched first, so they are probably over-represented in our sample.)
• “If we increase the sample size to 10, would that make the sample more representative?” (No, in fact, it may increase the over-representation of the longer straws and be even more misleading.)

Tell students that a larger sample does not help the estimate if the selection process is flawed. For example, if someone uses the heights of 40 basketball players instead of only 20 basketball players to determine average height of everyone in the United States, the larger sample probably does not represent the population any better.

Explain that, although the process may seem random since we took out as much of the human element of the choosing process as possible, the longer straws were over-represented in our samples. It is important to try to anticipate all the different ways that the selection process might be biased to avoid it as much as possible.

In this activity, students determine whether alternate methods of selecting items for a sample from the same population are fair (MP3). For the methods that work, the physical objects are linked with numerical values to remove even more of the bias toward selecting certain objects more often than others.

Tell students that a random sample from a population is a sample that is selected in a way that gives every different possible sample of the same size an equal chance of being the sample selected.

• “Which of the four methods proposed would be a random sample?” (putting the papers in the bag or using the spinner)
• “Would the techniques described here work for other situations in which we wanted a sample? For example, would they work to select 50 people in a large city to represent the views of the city residents?” (Although they would work in theory for large populations, it would be too time-consuming to write over a million numbers [or names] on pieces of paper and put them in a bag. Similarly, a spinner that is divided into a million sections would be difficult to manage. Computers can be used to generate random numbers for larger populations.)
• “The most common straw in the bag is the 2-inch straw. When selecting one of the straw numbers (not lengths) at random, what is the probability of selecting a 2-inch straw?” (, since there are 8 straws that are 2 inches long and 35 total straws)

Explain that:

• A representative sample would have more of the more common lengths, and there is also a higher probability of selecting these lengths, so a random selection should be a good way to select a representative sample.
• A random sample does not guarantee a representative sample, but it avoids methods that might over- or under-represent items of the population. Because we do not know the data for the population, a random sample usually provides the best opportunity to get a representative sample.
• While it is the most ideal method, it is not always possible to generate a random sample. For example, if we wanted to know the average size of salmon in the wild, it is impossible to know how many there are, much less identify them individually, select a few at random from the list, then capture and measure those exact individuals. In these cases, it is important to try to intentionally reduce bias as much as possible when selecting the sample.