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Unformatted text preview: Chapter 3 61 1 Chapter 3 Data Summary Using Descriptive Measures CHAPTER OVERVIEW AND OBJECTIVES Chapter 2 examined techniques for visually describing a set of data. The purpose of this chapter is to introduce techniques for describing a set of data using one or more numerical measures. By the end of the chapter, the student should be able to define and use the following measures: 1. Measures of Central Tendency: Mean, Median, Mode and Midrange. 2. Measures of Variation: Range, Standard Deviation, Variance, and Coefficient of Variation. 3. Measures of Position: Percentiles, Quartiles, and zscores. 4. Measures of Shape: Skewness and Kurtosis. 5. Measures of Relationship: Correlation and Covariance 6. Construction of box plots. 61 Instructor's Manual Chapter 3 Glossary bivariate data. Data recorded for a pair of variables, X and Y. box plot . A diagram that demonstrates the lowest and highest values within that portion of the sample not containing outliers, the three sample quartiles, and any sample values determined to be outliers. Chebyshev's inequality . A rule stating at least what percentage of the sample values are within 2, 3, standard deviations of the mean.\ coefficient of correlation. A measure of the strength of the linear relationship that exists within a sample of bivariate data. coefficient of variation . The sample standard deviation divided by the sample mean and multiplied by 100. covariance . The numerator of the formula for the correlation. The covariance has the same sign as the correlation. descriptive measure . A statistic that describes the location, variation, or shape of a sample or one that describes the position of an individual value in a sample (such as a percentile). empirical rule . A rule that states approximately what percentage of the sample values are within 1, 2, and 3 standard deviations of the mean. This rule assumes that the population has a bellshaped (normal) appearance. interquartile range . The difference between the first and third quartiles (Q 3 Q 1 ). kurtosis . A measure of shape that describes the tendency of a distribution to stretch out in a particular direction. mean . The average of the sample data; its symbol is x. measure . See descriptive measure . Measures consist of measures of central tendency, variation, position, and shape. measures of central tendency . Measures that describe the location (typical value) of a sample, including the sample mean, median, midrange, and mode. measures of variation . Measures that describe the variation within a sample; they include the sample range, variance, standard deviation, and coefficient of variation. 62 62 Chapter 3 63 measures of position . Measures that indicate the relative position of a sample value, such as percentiles, quartiles, and zscores....
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 Fall '11
 Pavur

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