Home of www.mathoninfo.net or The Mart or Commercial PagesStatistics 101Introductory Definitions

Introductory Definitions 1. Statistics is the study of data. 2. Descriptive statistics describes a set of data. 3. Inferential statistics generates estimates and predictions from a set of data. 4. A population is a set of objects or events being studied. 5. A sample is a subset of the population. 6. A variable is a characteristic of each unit (element) of the population (such as height for the human population). 7. A statistical inference is an estimate or prediction. 8. Reliability of an estimate or prediction is a statement of its probability. 9. Quantitative data are data expressed in units of measure (such as distance). 10. Qualitative data are data expressed in categories. (An example of quantitative data for a human population are the number of years of academic study completed; an example of qualitative data for a human population are the highest degrees obtained (bachelors, masters, doctorate.) 11. A representative sample is a sample that exhibits characteristics in proportion to those found within the population. Introductory Notational Definitions 12. An unordered set is denoted by braces {}. For example, {5.4, 3.1, 2.2}. In unordered set notation, there appear no duplicates. An unordered set may be used, for example, to denote a set of possible outcomes in an experiment. 13. An ordered set is denoted by parentheses (). For example, (5.4, 3.1, 5.4, 2.2). In an ordered set, duplicates may appear; here, we see 5.4 twice. Ordered sets are often used to list observed data. 14. Parentheses () are also used to denote open intervals of real numbers, i.e., intervals of real numbers that do not include the endpoints. Examples are: a. (0,1) denotes the set of all real numbers between 0 and 1, not including 0 and 1. b. (1,) denotes the set of all real numbers greater than 1. c. (-,1) denotes the set of all real numbers less than 1. Open intervals may also be denoted using the notation a < x < b or x > a. The above examples in this notation are: a. 0 < x < 1 denotes the set of all real numbers between 0 and 1, not including 0 and 1. b. 1 < x < or 1 < x or x > 1 denotes the set of all real numbers greater than 1. Note that (1,) and 1 < x < and 1 < x and x > 1 all denote the same interval (all real numbers greater than 1). All four notations are used frequently. 15. Brackets [] are used to denote closed intervals of real numbers, i.e., intervals of real numbers that include the endpoints. For example, [0,1] denotes the set of all real numbers between 0 and 1, including 0 and 1. Closed intervals may also be denoted using the notation a x b; for example, the interval [0,1] may be denoted by 0 x 1.

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