The value of Young’s modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations (“Strength and Modulus of a Molybdenum-Coated Ti-25Al-10Nb-3U- 1Mo Intermetallic,” J. of Materials Engr. and Performance, 1997: 46–50): a?. ?Calculate and the deviations from the mean. b?. ?Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation. c.? ?Calculate ?s?2 by using the computational formula for the numerator ?S?xx. d?. ?Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance of these transformed values, and compare it to s?2 for the original data.

Answer: Step 1 of 4 a. Calculate and the deviations from the mean. x - x Sl. No x 1 116.4 0.82 2 115.9 0.32 3 114.6 -0.98 4 115.2 -0.38 5 115.8 0.22 SUM 577.9 0 AVERAGE (x) 115.58 Notice that the deviations from the mean sum to zero, as they should. Step 2 of 4 b. Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation. (x - x ) 2 Sl. No x x 1 116.4 0.6724 13548.96 2 115.9 0.1024 13432.81 3 114.6 0.9604 13133.16 4 115.2 0.1444 13271.04 5 115.8 0.0484 13409.64 SUM 577.9 1.928 66795.61 AVERAGE (x) 115.58 The sample variance S2 from the definition (x x ) 2 s = n 1 1.928 = 4 = 0.482 Sample standard deviation is the square root of the sample standard deviation. (x x ) s = n 1 = 0.482 = 0.6942