Sampling Methods Lesson 3-6 Pg. # 103-105 CA Content Standards Statistics, Data Analysis, and Probability 2.2***: I can identify different ways of selecting a sample (i.e. convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population. Statistics, Data Analysis, and Probability 2.4***: I can identify data that represent sampling errors and explain why the sample might be biased. Vocabulary: BIASED Survey results in which samples are chosen or used unfairly. Vocabulary: REPRESENTATIVE Containing typical examples of all types in a group. Vocabulary: CONVENIENCE SAMPLING Sample is formed by choosing individuals or objects that are convenient, or easy, to include in the study. Usually results in a biased sample. Vocabulary: RANDOM SAMPLING Sampling in which each individual or item has an equal chance of being chosen. Usually results in a representative, or fair, sample. Vocabulary: SYSTEMATIC SAMPLING Sampling that involves a system, method, or plan. Usually results in a representative, or fair, sample. Vocabulary: RESPONSES TO A SURVEY Answers to a questionnaire or other device designed to get information from a population. Usually results in a biased sample because only people who really care or have the time will respond to the survey. Objective Understand how the method of sampling determines how representative the sample is of the population. Math Link: You can use what you know about sampling to find how sampling methods can affect the statistical results. Example 1. Look at the table on page 103. It shows the number of school districts in each state. The five most populated states are California (CA), Texas (TX), Michigan (MI), Illinois (IL), and New York (NY). Find the median number of school districts per state using these five states as a sample. MI NY IL CA TX 674 705 929 994 1042 The median is the middle number in the sample. According to this sample, there are approximately 929 school districts in each state. A biased sample does not reflect the population fairly. This sample is biased because states with large populations are likely to have more than an average number of school districts. Example 2. The name of each state was written on a piece of paper and placed in a bag. Then five pieces of paper were selected without looking. The states selected were Maine (ME), Colorado (CO), Wisconsin (WI), Kansas (KS), and Rhode Island (RI). RI CO ME KS WI 36 176 284 304 426 The median is the middle number in the sample. According to this sample, there are approximately 284 school districts in each state. This example uses random sampling. In random sampling, each school district has an equal chance of being chosen. Since a random sample is usually a good match for the population, it is a representative sample. Example 3. The principal of an elementary school sent a survey letter to each student’s parents asking if voters in the school district would support a tax increase to build a new middle school. Is this sample likely to be representative or biased? The sample is biased. Parents of elementary students who would be attending the new school are more likely to support a new middle school than would voters in general. It was convenient for the principal to survey parents of students. In convenience sampling, any easy method is used to choose the sample. This is usually biased. Asking for responses to a survey is another form of sampling that is often biased. People with strong opinions are more likely to take the time to respond to a survey than people in general. Example 4. Cassie wants to determine which brand of athletic shoes is most popular with U.S. middle school students. She decides to stand near the entrance of her school and keep a count of what brands of shoes students are wearing as they enter the school. What sampling method is Cassie using? Convenience Sampling Is it likely to be representative or biased? Why? It is likely to be biased since she is studying only students at her school. The Moral of the Story: Random sampling is important for obtaining measures that accurately describe the population being studied. Convenience sampling and responses to surveys involve a bias.
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