Introduction for Beginning Statistics
Practice problems for these concepts can be found at:
- Introduction Solved Problems for Beginning Statistics
- Introduction Supplementary Problems for Beginning Statistics
Statistics is a discipline of study dealing with the collection, analysis, interpretation, and presentation of data. Pollsters who sample our opinions concerning topics ranging from art to zoology utilize statistical methodology. Statistical methodology is also utilized by business and industry to help control the quality of goods and services that they produce. Social scientists and psychologists use statistical methodology to study our behaviors. Because of its broad range of applicability, a course in statistics is required of majors in disciplines such as sociology, psychology, criminal justice, nursing, exercise science, pharmacy, education, and many others. To accommodate this diverse group of users, examples and problems in this outline are chosen from many different sources.
The use of graphs, charts, and tables and the calculation of various statistical measures to organize and summarize information is called descriptive statistics. Descriptive statistics help to reduce our information to a manageable size and put it into focus.
EXAMPLE 1.1 The compilation of batting average, runs batted in, runs scored, and number of home runs for each player, as well as earned run average, won/lost percentage, number of saves, etc., for each pitcher from the official score sheets for major league baseball players is an example of descriptive statistics. These statistical measures allow us to compare players, determine whether a player is having an "off year" or "good year," etc.
EXAMPLE 1.2 The publication entitled Crime in the United States published by the Federal Bureau of Investigation gives summary information concerning various crimes for the United States. The statistical measures given in this publication are also examples of descriptive statistics and they are useful to individuals in law enforcement.
Inferential Statistics: Population and Sample
The population is the complete collection of individuals, items, or data under consideration in a statistical study. The portion of the population selected for analysis is called the sample. Inferential statistics consists of techniques for reaching conclusions about a population based upon information contained in a sample.
EXAMPLE 1.3 The results of polls are widely reported by both the written and the electronic media. The techniques of inferential statistics are widely utilized by pollsters. Table 1.1 gives several examples of populations and samples encountered in polls reported by the media. The methods of inferential statistics are used to make inferences about the populations based upon the results found in the samples and to give an indication about the reliability of these inferences. Suppose the results of a poll of 600 registered voters are reported as follows: Forty percent of the voters approve of the president's economic policies. The margin of error for the survey is 4%. The survey indicates that an estimated 40% of all registered voters approve of the economic policies, but it might be as low as 36% or as high as 44%.
EXAMPLE 1.4 The techniques of inferential statistics are applied in many industrial processes to control the quality of the products produced. In industrial settings, the population may consist of the daily production of toothbrushes, computer chips, bolts, and so forth. The sample will consist of a random and representative selection of items from the process producing the toothbrushes, computer chips, bolts, etc. The information contained in the daily samples is used to construct control charts. The control charts are then used to monitor the quality of the products.
EXAMPLE 1.5 The statistical methods of inferential statistics are used to analyze the data collected in research studies. Table 1.2 gives the samples and populations for several such studies. The information contained in the samples is utilized to make inferences concerning the populations. If it is found that 245 of 350 or 70% of prison inmates in a criminal justice study were abused as children, what conclusions may be inferred concerning the percent of all prison inmates who were abused as children? The answers to this question are found in Chapters 8 and 9.
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