Fretting is a wear process that results from tangential oscillatory movements of small amplitude in machine parts. The article “Grease Effect on Fretting Wear (10-4 mm3)of Mild Steel” (?Industrial Lubrication and Tribology?, 2008: 67–78) included the following data on volume wear for base oils having four different viscosities. a?. ?The sample coefficient of variation100s?x ?assesses the extent of variability relative to the mean (specifically, the standard deviation as a percentage of the mean).Calculate the coefficient of variation for the sample at each viscosity. Then compare the results and comment. b?. ?Construct a comparative boxplot of the data and comment on interesting features.

Answer : Step 1 of 3 : Fretting is a wear process that results from tangential oscillatory movements of small amplitude in machine parts. The article “Grease Effect on Fretting Wear (10-4 mm3)of Mild Steel” , included the following data on volume wear for base oils having four different viscosities. Viscosity Wear 20.4 58.8 30.8 27.3 29.9 17.7 76.5 30.2 44.5 47.1 48.7 41.6 32.8 18.3 89.4 73.3 57.1 66 93.8 133.2 81.1 252.6 30.6 24.2 16.6 38.9 28.7 23.6 Step 2 of 3 : a) The claim is to find the coefficient of variation. For that we have to find mean and standard deviation of each viscosity The formula for coefficient of variance = (s/x)100 So first we have to find the mean and standard deviation of the wear for each viscosity. xi Where, mean = n and s = variance Viscosity x s cv 20.4 40.17 22.50 56.01 30.2 38.83 11.52 29.66 89.4 84.083 27.16 32.30 252.6 27.1 7.55 27.86 The sample coefficient of variation is similar for the three highest oil viscosity levels (29.66, 32.30, 27.86) but is much higher for the lowest viscosity (56.01). At low viscosity, it appears that there is much more variation in volume wear relative to the average or “typical” amount of wear.