The mathematical purpose of this lesson is for students to understand the importance of randomness in selecting a sample and the importance of randomness in assigning participants to groups for an experimental study. The work of this lesson connects to prior work because students investigated what it means to be random in a statistical sense and how to select at random. The work of this lesson connects to upcoming work because students will describe distributions, use standard deviation as a measure of variability, and investigate normal distributions, all of which rely on understanding the nature of randomness. Students encounter the term random selection which is a term used to describe a selection process by which each item in a set has an equal probability of being selected, and the term sample which is defined as a group that is selected from the whole population. When students describe the importance of randomness in selecting samples and dividing groups in the context of a study, they are attending to precision (MP6).
- Comprehend (in spoken and written language) what it means to be random in the context of statistics.
- Explain (orally and in writing) what it means to select at random.
- Let’s explore why randomness is important in studies.
All students will need a random number generator (for example, a calculator, spreadsheet, or randomly drawing numbered pieces of paper will work) that can generate whole numbers between 1 and 100. You will need to collect data from each student to create four data sets so you can make a dot plot from each data set.
- I recognize that the way I choose a sample matters, and that random samples have less bias.
An experimental study collects data by directly influencing something to determine how another thing is changed.
An observational study collects data without influencing the subjects directly.
A selection process by where each item in a set has an equal probability of being selected.
A sample is a subset of a population.
A survey is a set of questions given to people to seek their responses.