Indeed, the sample median would remain unchanged if these values were replaced by any other five values greater than or equal to 259. The reason for this is that whereas the sample mean for the first set is greatly affected by the five data values greater than 500, these values have a much smaller effect on the sample median. Thus, whereas the sample mean is quite a bit larger for the first data set, the sample medians are approximately equal. On the other hand, since there are 29 data values for the germ-free mice, the sample median is the 15th largest data value, namely, 259 similarly, the sample median for the other set of mice is the 10th largest data value, namely, 265. It is clear from the stem and leaf plots that the sample mean for the set of mice put in the germ-free setting is larger than the sample mean for the set of mice in the usual laboratory setting indeed, a calculation gives that the former sample mean is 344.07, whereas the latter one is 292.32. Ross, in Introduction to Probability and Statistics for Engineers and Scientists (Fourth Edition), 2009 SOLUTION These within-group values can be quite valuable to help you discover patterns in the data, such as that all the data values are multiples of some common value, or find out which values occur most frequently within a stem group. (If the size of the data set were very large, then, from a practical point of view, the values of all the leaves might be too overwhelming and a stem-and-leaf plot might not be any more informative than a histogram.) Physically this plot looks like a histogram turned on its side, with the additional plus that it presents the original within-group data values. It is most helpful in moderate-size data sets. Stem-and-leaf plots are quite useful in showing all the data values in a clear representation that can be the first step in describing, summarizing, and learning from the data. It is clear from this plot that almost all the data values are between 100 and 200, and the spread is fairly uniform throughout this region, with the exception of fewer values in the intervals between 100 and 110 and between 190 and 200. Note that a stem without any leaves (such as stem value 23) indicates that there are no occurrences in that class. They tell us, for instance, that there are 10 values having stem 16 that is, 10 individuals have weights between 160 and 169. The numbers in parentheses on the right represent the number of values in each stem class.
0 Comments
Leave a Reply. |