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DATA MANAGEMENT MBF3C Lesson #1: Sampling Types and Techniques

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Unit Learning Goals 1. To calculate the mean, median and mode of a group of numbers 2. To calculate the variaMATHEMATICAL models 3. To show an understanding of probability and its real-world significance. 4. To collect, organize, analyse and evaluate data

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YOUR TEXTBOOK Pages

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LESSON Learning Goals 1. To explain the difference between the terms population and sample 2. To describe the characteristics of a good sample 3. To explain why sampling is necessary (e.g., time, cost, or physical constraints) 4. To describe and compare sampling techniques (e.g. random, stratified, clustered, convenience, voluntary); 5. To explain how to collect one-variable data from primary sources, using appropriate sampling techniques in a variety of real-world situations; 6. To explain how to organize and store the data;

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INTRODUCTION When conducting a survey, it is important to choose the right questions to ask and to select the appropriate group to survey. Before a market research department designs a survey, the target group for the survey needs to be identified.

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There are 300 students taking mathematics this semester at Royal Secondary School. The table shows the number of mathematics students in each grade. Mrs. Barron, the principal, wishes to survey a total of 60 mathematics students. She has chosen 20 grade 9s, 16 grade 10s, 15 grade 11s, and 9 grade 12s.

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1. Calculate the percent of the population that each grade represents. 2. Calculate the percent of the sample that each of Mrs. Barron’s choices represents.

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3. Mrs. Barron decides to select each student for the sample using a random number generator on her graphing calculator. Help her select the grade 9 students.

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Population and Sample It is usually impractical to survey every member of a target group or population, so only a sample of the population is surveyed. Population all individuals or items that belong to a group being studied Sample a group of individuals or items that are representative of the population from which they are taken

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THERE ARE A NUMBER OF DIFFERENT WAYS TO CHOOSE A SAMPLE: 1. Simple Random Sample Each member of the population has an equal chance of being selected. 2. Stratified Random Sample The population is divided into subgroups (for example, by gender, age, nationality) and a random sample is selected from each subgroup in proportion to its size in the population. 3. Voluntary-Response Sample The sample contains those members of the population who have chosen to respond to the survey. 4. Cluster Sample: The population is divided into clusters and a certain number of clusters are chosen. Every member of these clusters is part of the sample. 5. Convenience Sample The sample contains those members of the population from which data are most easily collected. 6. Systematic Sample Every nth member of the population is selected.

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Types of Sampling Simple Random Sample Stratified Random Sample Cluster sampling Systematic Convenience

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Use random sampling to draw inferences about a population. 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.

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Simple Random Sample Every subset of a specified size n from the population has an equal chance of being selected

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Stratified Random Sample The population is divided into two or more groups called strata, according to some criterion, such as geographic location, grade level, age, or income, and subsamples are randomly selected from each strata.

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Cluster Sample The population is divided into subgroups (clusters) like families. A simple random sample is taken of the subgroups and then all members of the cluster selected are surveyed.

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Systematic Sample Every nth member ( for example: every 10th person) is selected from a list of all population members.

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Convenience Sample Selection of whichever individuals are easiest to reach It is done at the “convenience” of the researcher

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In-Class/Homework Page , Q#1-12

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