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10descsd

# 10descsd - Accountability Modules WHAT IT IS Return to...

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Accountability Modules Data Analysis: Describing Data - Descriptive Statistics Texas State Auditor's Office, Methodology Manual, rev. 5/95 Data Analysis: Describing Data - Descriptive Statistics - 1 WHAT IT IS Descriptive statistics include the numbers, tables, charts, and graphs used to Return to Table of Contents describe, organize, summarize, and present raw data. Descriptive statistics are most often used to examine: central tendency (location) of data, i.e. where data tend to fall, as measured by the mean, median, and mode. dispersion (variability) of data, i.e. how spread out data are, as measured by the variance and its square root, the standard deviation. skew (symmetry) of data, i.e. how concentrated data are at the low or high end of the scale, as measured by the skew index. kurtosis (peakedness) of data, i.e. how concentrated data are around a single value, as measured by the kurtosis index. Any description of a data set should include examination of the above. As a rule, looking at central tendency via the mean, median, and mode and dispersion via the variance or standard deviation is not sufficient. (See the definitions below for more details.) DEFINITIONS The following definitions are vital in understanding descriptive statistics: Variables are quantities or qualities that may assume any one of a set of values. Variables may be classified as nominal, ordinal, or interval. Nominal variables use names, categories, or labels for qualitative values. Typical nominal variables include gender, ethnicity, job title, and so forth. Ordinal variables, like nominal variables, are categorical variables. However, the order or rank of the categories is meaningful. For example, staff members may be asked to indicate their satisfaction with a training course on an ordinal scale ranging from “poor” to “excellent.” Such categories could be converted to a numerical scale for further analysis. Interval variables are purely numeric variables. The nominal and ordinal variables noted above are discrete since they do not permit making statements about degree, e.g., “Person A is three times more male than person B” or “Person A rated the course as five times more excellent than person B.” Interval variables are continuous, and the difference between values is both meaningful and allows statements about extent or degree. Income and age are interval variables. Frequency distributions summarize and compress data by grouping them into classes and recording how many data points fall into each class. The frequency distribution is the foundation of descriptive statistics. It is a prerequisite for the various graphs used to display data and the basic statistics used to describe a data set, such as the mean, median, mode, variance, standard deviation, etc. (See the module on Frequency Distribution for more information.) Measures of Central Tendency indicate the middle and commonly occurring points in a data set. The three main measures of central tendency are discussed below.

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