Data Collection. MATH 130, Elements of Statistics I. J. Robert Buchanan. Fall Department of Mathematics

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1 Data Collection MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018

2 Big Definition Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. Statistics also provides a measure of confidence in any conclusions.

3 Process of Statistics 1. Identify the research objective (the question to be answered). The group to be studied is called a population which is composed of individuals. 2. Collect the data needed to answer the question. Data are collected from a subset of the population called a sample. A statistic is a numerical summary of a sample. 3. Organize, summarize, and describe the data (called descriptive statistics). 4. Perform an inference or draw conclusions about the population from the information (called inferential statistics). A parameter is a numerical summary of a population.

4 Example (1 of 2) The AP-National Constitution Center conducted a poll August 11-16, 2010, to learn how adult Americans feel existing gun-control laws infringe on the second amendment to the U.S. Constitution. 1. Identify the research objective. The researchers wished to determine the percentage of adult Americans who believe gun-control laws infringe on the public s right to bear arms. The population being studied was adult Americans. 2. Collect the data. It is unreasonable to expect to survey more than 200 million adult Americans, so the researchers surveyed a sample of 1007 adult Americans. Of those surveyed, 514 stated they believe existing gun-control laws infringe on the public s right to bear arms. 3. Describe the data. Of the 1007 individuals in the survey, 51% ( %) believe existing gun-control laws infringe on the public s right to bear arms. This is a statistic because its value was determined from a sample.

5 Example (2 of 2) 4. Perform inference. The researchers at the AP-National Constitution Center wanted to extend the results of the survey to all adult Americans. Remember, when generalizing results from a sample to a population, the results are uncertain. To account for this uncertainty, researchers reported a 3% margin of error. This means the researchers feel fairly certain (in fact 95% certain) that the percentage of all adult Americans who believe existing gun-control laws infringe on the public s right to bear arms is somewhere between 48% and 54%.

6 Variables Definition A variable is a characteristic of interest about the individuals in a population. Example height weight hair color income zip code

7 Qualitative vs. Quantitative Variables Definition Qualitative (or categorical) variables allow for classification of individuals based on some attribute or characteristic. Definition Quantitative variables provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted and provide meaningful results.

8 Example Identify each of the following as an example of a qualitative or quantitative variable. 1. The breaking strength of a piece of string. 2. The number of stop signs in towns of less than 500 people. 3. The hair color of children auditioning for a play. 4. Whether or not a faucet is defective. 5. The number of questions answered correctly on a standardized test. 6. The length of time spent on hold to have a question answered by the help desk via telephone.

9 Continuous vs. Discrete Variables Definition A discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting 0, 1, 2, 3, and so on. Discrete variable values generally have gaps between them. Definition A continuous variable is a quantitative variable that has an infinite number of possible values that are not countable. There are generally no gaps between the values that a continuous variable may take on.

10 Example Identify each of the following as an example of a discrete or continuous variable. 1. A poll of registered voters about which candidate they will support. 2. The length of time required for a wound to heal after a bandage is applied. 3. The number of telephone calls received by a help desk in a 10-minute period. 4. The distance freshmen can kick a football. 5. The number of pages in term papers written for ENGL The kind of tree used as a Christmas tree.

11 Variables, Values, and Data The list of observed values for a variable is data. Qualitative data are observations corresponding to a qualitative variable. Quantitative data are observations corresponding to a quantitative variable. Discrete data are observations corresponding to a discrete variable. Continuous data are observations corresponding to a continuous variable.

12 Example Country Government Type Life Expectancy Population (years) (in millions) Australia Federal parliamentary democracy Canada Constitutional monarchy France Republic Morocco Constitutional monarchy Poland Republic Sri Lanka Republic United States Federal republic Identify the individuals, variables, and data in this table.

13 Level of Measurement of a Variable A variable is at the nominal level of measurement if the values of the variable name, label, or categorize. A variable is at the ordinal level of measurement if it has the properties of the nominal level of measurement and the values of the variable can be ranked. A variable is at the interval level of measurement if it has the properties of the ordinal level of measurement and differences in the values of the variable have meaning. A value of zero does not mean the absence of the quantity. Arithmetic operations such as addition and subtraction can be performed on the values of the variable. A variable is at the ratio level of measurement if it has the properties of the interval level of measurement and ratios of the values of the variables have meaning. A value of zero means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable.

14 Determining the Level of Measurement Identify the level of measurement for each of the following types of data. 1. In a sample of stereo speakers, 12 were rated good, 16 were rated better, and 8 were rated best. 2. Zip codes. 3. Weights of plastic discarded by households. 4. The years 1000, 2000, 1776, 1941, and Movies listed according to their genre, such as comedy, adventure, romance, martial arts. 6. Room temperatures (measured in C). 7. Math courses College Algebra, Elements of Statistics, and Business Calculus. 8. Lengths (measured in minutes) of movies. 9. Social security numbers. 10. Differences in skiing times between skiers in the down-hill slalom event and the current world record.