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 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.

Step 1 of 4</p>

a) We have to find the deviations from mean

The given values 116.4, 115.9, 114.6, 115.2, 115.8

Now Mean (

=(116.4+115.9+114.6+115.2+115.8)/5

=577.9/5

= 115.58

The deviations from mean is

Step 2 of 4</p>

b) We have to find sample variance and sample standard deviation from the deviations

Now sample variance (s)=

=(0.82)2+(0.32)2+(-0.98)2+(-0.38)2+(0.22)2/4

=1.928/4

=0.482

The sample standard deviation (s)=

=

= 0.69

Hence sample variance=0.482 and the sample standard deviation=0.69