42 The value of Young s modulus GPa was determined for cast

42. The value of Young s modulus (GPa) was deter-mined for cast plates consisting of certain inter-metallic substrates, resulting in the following sample observations ( Strength and Modulus of a Molybdenum-CoatedTi-25Al-10Nb-3U-1MoInter-metallic, J. Mater. Engrg. Perform., 1997: 46—50):

116.4 115.9 114.6 115.2 115.8

a. Calculate and the deviations from the mean.

b. Use the deviations calculated in part (a) to ob-tain 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.

Solution

a) Mean = 115.58

Std dev =0.62097

Variance = 0.3856

--------------------------------------------------

b) Sample variance = 0.482

Sample std dev = 0.69426

c) Sampel variance (x_100) = Sampe variance of X = 0.69426