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Statistics and More

Statistics is the gathering, organization, analysis, and presentation of numerical information. You can apply statistical methods to almost any kind of data. Researchers, advertisers, professors, and sports announcers all make use of statistics. Often, researchers gather large quantities of data since larger samples usually give more accurate results. The first step in the analysis of such data is to find ways to organize, analysis, and present the information in an understandable form.

The unprocessed information collected for a study is called raw data. The quantity being measured is the variable. A continuous variable can have any value within a given range, while a discrete variable can have only certain separate values (often integers). For example, the height of students in your school is a continuous variable, but the number in each class is a discrete variable. Often, it is useful to know how frequently the different values of a variable occur in a set of data. Frequency tables and frequency diagrams can give a convenient overview of the distribution of values of the variable and reveal trends in the data.

A histogram is a special form of bar graph in which the areas of the bars are proportional to the frequencies of the values of the variable. The bars in a histogram are connected and represent a continuous range of values. Histograms are used for variables whose values can be arranged in numerical order, especially continuous variables, such as weight, temperature, or travel time. Bar graphs can represent all kinds of variables, including the frequencies of separate categories that have no set order, such as hair color or citizenship. A frequency polygon can illustrate the same information as a histogram or bar graph. To form a frequency polygon, plot frequencies versus variable values and then join the points with straight lines.

A cumulative-frequency graph or ogive shows the running total of the frequencies from the lowest value up.

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