In this lesson, students consider different methods of selecting a sample. Students begin by critiquing different sampling methods for their benefits and drawbacks. In particular, students notice that some sampling methods are more biased than others. A follow-up activity shows that some methods may seem to be unbiased at first, but have a hidden bias that restricts the sample from being representative of the population. Finally, students practice recognizing when a sampling method is likely to be biased (MP3), and they see that selecting a sample at random is more likely to produce a representative sample.
- Describe (orally and in writing) methods to obtain a random sample from a population.
- Justify (orally) whether a given sampling method is fair.
- Recognize that random sampling tends to produce representative samples and support valid inferences.
Let’s explore ways to get representative samples.
For the That’s the First Straw activity, prepare one paper bag containing straws cut to the specified lengths in the table for a demonstration.
The demonstration will also require a ruler marked with inches to measure the straw pieces chosen in a sample.
- I can describe ways to get a random sample from a population.
- I know that selecting a sample at random is usually a good way to get a representative sample.
The mean is one way to measure the center of a data set. We can think of it as a balance point. For example, for the data set 7, 9, 12, 13, 14, the mean is 11.
To find the mean, add up all the numbers in the data set. Then, divide by how many numbers there are. \(7+9+12+13+14=55\) and \(55 \div 5 = 11\).
mean absolute deviation (MAD)
The mean absolute deviation is one way to measure how spread out a data set is. Sometimes we call this the MAD. For example, for the data set 7, 9, 12, 13, 14, the MAD is 2.4. This tells us that these travel times are typically 2.4 minutes away from the mean, which is 11.
To find the MAD, add up the distance between each data point and the mean. Then, divide by how many numbers there are.
\(4+2+1+2+3=12\) and \(12 \div 5 = 2.4\)
The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.
For the data set 7, 9, 12, 13, 14, the median is 12.
For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. \(6+8=14\) and \(14 \div 2 = 7\).
A population is a set of people or things that we want to study.
For example, if we want to study the heights of people on different sports teams, the population would be all the people on the teams.
A sample is representative of a population if its distribution resembles the population's distribution in center, shape, and spread.
For example, this dot plot represents a population.
This dot plot shows a sample that is representative of the population.
A sample is part of a population. For example, a population could be all the seventh grade students at one school. One sample of that population is all the seventh grade students who are in band.