STATISTICS AND PROBABLITY 2 The article A ThinFilm Oxygen Up

STATISTICS AND PROBABLITY

2. The article A Thin-Film Oxygen Uptake Test for the Evaluation of Automotive Crankcase Lubricants (Lubric. Engr., 1984: 75?83) reported the following data on oxidation-induction time (mm) for various commercial oils: 87 103 130 160 180 195 132 145 211 105 145 153 152 138879993 119 129 a. Calculate the sample variance and standard deviation. b. If the observations were reexpressed, in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the reexpression.

Solution

X (X-mean)^2 hours 87 2693.0637179202 1.45 0.6371960603 103 1288.4321371202 1.7166666667 0.2825761772 130 79.1163445202 2.1666666667 0.0066551246 160 445.4321305202 2.6666666667 0.1750761773 180 1689.6426545202 3 0.5651346569 195 3147.8005475202 3.25 1.0035118499 132 47.5373969202 2.2 0.0023276393 145 37.2742375202 2.4166666667 0.028365651 211 5199.1689667202 3.5166666667 1.6088919668 105 1148.8531895202 1.75 0.2482486919 145 37.2742375202 2.4166666667 0.028365651 153 198.9584471202 2.55 0.0910557095 152 171.7479209202 2.5333333333 0.0812750077 138 0.8005541202 2.3 0.0026785165 87 2693.0637179202 1.45 0.6371960603 99 1591.5900323202 1.65 0.3578978147 93 2106.3268751202 1.55 0.4875469375 119 395.8005563202 1.9833333333 0.0701785164 129 97.9058183202 2.15 0.0096522007 mean 134.8947368421 2.248245614 variance 1214.1994464465 0.3328331794 standard deviation 34.8453647771 0.5769169606