Section 1.2: Data, Sampling, Variation in Data and Sampling

Section 1.2: Data, Sampling, Variation in Data and Sampling Goals: 1) Determine if data are qualitative (categorical) or quantitative 2) Determine if data are quantitative discrete or quantitative continuous 3) Be able to identify the type of sampling used when creating a sample Why are these skills important? Data Quantitative (Numerical) Qualitative (Categorical) Discrete Continuous Data sheets Types of Graphs used with Qualitative Data Sampling Sampling is the process of selecting individuals (or objects) from a population in order to construct a sample. Samples should have the same characteristics of the population from which they are drawn. In other words, samples should be representative of the population. Sampling With Replacement occurs when objects (individuals) may be selected more than once. A selection is made and then that selection is placed back into the population. In this scenario, the size of the population prior to every selection is the same. Sampling Without Replacement occurs when objects (individuals) may only be selected one time. Once an individual is chosen, that individual may not be selected again. After each selection, the size of the population decreases by 1. Random Sample: A sample in which every member of the population has the same chance of being selected for the sample. Ideally, every sampling technique should have randomness built into it. Simple Random Sample: A sample in which every sample of size n have the same chance of being selected. Sampling (random vs. simple random) An instructor wants to create a sample of 5 students from a class of 25 students. For each of the following examples, determine if the sample is a random sample and a simple random sample. 1) The roster is alphabetized and each student is assigned a number 1 through 25. 5 numbers are then randomly generated. The sample consists of those students paired with each of the 5 randomly generated numbers. 2) The class is arranged in 5 rows of 5 students each. One student from each row is randomly selected. 3) The class is arranged in 5 rows of 5 students each. A row is randomly selected and all students in that row become the sample. Sampling Stratified Sample: A sample constructed after the population is divided into mutually exclusive subgroups, call strata. Members are randomly selected from each subgroup to form the sample. Cluster Sample: Similar to a stratified sample in that the population is divided into mutually exclusive subgroups. However, instead of selecting individuals from each subgroup, entire subgroups are randomly selected to form the sample. Systematic Sample: A sample in which every kth member of the population is selected for the sample. Convenience Sample: A sample that is generated using individuals that are "convenient." Sampling Examples 1) A sample of 100 Skagit Valley College students is taken by randomly selecting 50 freshman and 50 sophomores. 2) A student is randomly selected from an alphabetized list of Skagit Valley College students. Starting with that student, a sample of Skagit Valley College students is created by selecting every 15th student until 100 students are chosen. 3) Each student in an alphabetized list of Skagit Valley College students is assigned a number. Then a random number generator is used to select 75 Skagit Valley College students. 4) An instructor stands outside of Oak Hall and asks the first 50 people walking by how many hours of sleep they got the night before. 5) Students are sorted based on the zip code of their address. A single zip code is randomly selected an all of those students in that zip code are in the sample. Considerations (page 20):