45. 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-3U1Mo Intermetallic,” J. of Materials Engr. and Performance, 1997: 46–50):

116.4 115.9 114.6 115.2 115.8

a. Calculate x 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 s2 by using the computational formula for the numerator Sxx.

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 s2 for the original data.