chapter 1

Chapter 1: Overview and Descriptive Statistics55.a. Lower half of the data set: 325 325 334 339 356 356 359 359 363 364 364366 369, whose median, and therefore the lower quartile, is 359 (the 7 th observation inthe sorted list).The top half of the data is 370 373 373 374 375 389 392 393 394 397 402403 424, whose median, and therefore the upper quartile is 392. So, the IQR = 392 -359 = 33.b. 1.5(IQR) = 1.5(33) = 49.5 and 3(IQR) = 3(33) = 99. Observations that are further than49.5 below the lower quartile (i.e., 359-49.5 = 309.5 or less) or more than 49.5 unitsabove the upper quartile (greater than 392+49.5 = 441.5) are classified as 'mild' outliers.'Extreme' outliers would fall 99 or more units below the lower, or above the upper,quartile. Since the minimum and maximum observations in the data are 325 and 424, weconclude that there are no mild outliers in this data (and therefore, no 'extreme' outlierseither).c. A boxplot (created by Minitab) of this data appears below. There is a slight positiveskew to the data, but it is not far from being symmetric. The variation, however, seemslarge (the spread 424-325 = 99 is a large percentage of the median/typical value)320370Escape time420d. Not until the value x = 424 is lowered below the upper quartile value of 392 would therebe any change in the value of the upper quartile. That is, the value x = 424 could not bedecreased by more than 424-392 = 32 units.27