概率与统计英文chapter Probability and Statistics.ppt

Solution: The list of ordered value is 7.6 8.3 9.3 9.4 9.4 9.7 10.4 11.5 11.9 15.2 16.2 20.4 Since n=12 is even The data set in example 11.4 illustrates an important property of in contrast to : The sample median is very insensitive to a number of extremely small or extremely large data values. If, for example, we increased the two largest xi’s from 16.2 and 20.4 to 26.2 and 30.4, respectively, would be unaffected. Thus, in the treatment of outlying data value, and are at opposite ends of a spectrum: is sensitive to even one such value, whereas is insensitive to a large number of outlying values. * Other Measures of Location: Quartiles, Percentiles, and Trimmed Means The median divides the data set into two parts of equal size. To obtain finer measures of location, we could divide the data into more than two such parts. Roughly speaking , quartiles divide the data set into four equal parts, with the observations above the third quartile constituting the upper quarter of the data set, the second quartile being identical to the median, and the first quartile separating the lower quarter from the upper three-quarters. Similarly, a data set can be divided into 100 equal parts using percentiles; the 99th percentile separates the highest 1% from the bottom99%, and so on. * 1.4 Measures of Variability Reporting a measure of center gives only partial information about a data set or distribution. Different samples or populations may have identical measures of center yet differ from one another in other important ways. * * * * * * * * 30 40 50 70 60 1 2 3 * Measures of Variability for Sample Data The simplest measure of variability in a sample is the range, which is the difference between the largest and smallest sample values. Our primary measures of variability involve deviations from the mean, Unfortunately, there is a major problem with this sugges