Defining Success Understanding Statistical Vocabulary

In this lesson we will be studying vocabulary that will allow us to: understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. (M.7.SP.1 /CCSS.7.SP.A.1) use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. (M.7.SP.2 /CCSS.7.SP.A.2)

Statistical Vocabulary Population Sample Sampling Techniques Bias Types of Data

Example For each situation described below is the variable quantitative or qualitative? a. People in a city are asked whether they support increasing the driving age to 18 years old. b. Compare the poverty rates of each country in the world.

Suppose you want to estimate the average number of hours that students in your school spend studying each week. Which of the following is the best method of sampling? a. Go to the honors classes at your school and ask all the students there how much they study. b. all students and ask them to fill out a survey on how much they study, and use all the data you get. c. Choose a sample of students you know that you think resembles the general population of students at your school. d. Anonymously survey each student in your class. Require all students to respond. e. Get a list of the student body and randomly select students to ask how much time they spend studying.

Solutions a. This would be a biased sample. Students in the honors courses are more likely to study more than the average student. b. Some students may choose to respond, and others may choose not to. The sample that responded are therefore not representative of all students since it is reasonable to imagine that students that don’t respond are likely to spend less time studying. This is called volunteer bias. c. Not a randomly selected sample. Humans are not good at picking samples that resemble the population. d. Your class is not representative of all students in the school. e. This seems like the best method to collect data. This is called simple random sampling.