Suppose the value of Young\'s modulus (GPa) was determined for cast plates consi

Question

Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations: (a) Calculate x. 11566 GPa Calculate the deviations from the mean. (Enter your answers to two decimal places.) (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 of transformed values. Now calculate the sample variance of these transformed values.

Explanation / Answer

Ans:

a)sample mean=(116.9+115.8+114.5+115.4+115.7)/5=578.3/5=115.66

deviations from mean:

(116.9-115.66),(115.8-115.66),(114.5-115.66),(115.4-115.66),(115.7-115.66)

1.24,0.14,-1.16,-0.26,0.04

b)Sample variance

sample variance=s2 =[(1.24)2+(0.14)2+(-1.16)2+(-0.26)2+(0.04)2]/(5-1)=2.972/4=0.743

sample standard deviation=sqrt(0.743)=0.862

c)

it will be same as above,s2 =0.743

d)After subtracting 100 from each value

16.9,15.8,14.5,15.4,15.7

mean=(16.9+15.8+14.5+15.4+15.7)/5=15.66

Variance=(16.9-15.66)2+(15.8-15.66)2+(14.5-15.66)2+(15.4-15.66)2+(15.7-15.66)2 /4

=(1.242+0.142+(-1.16)2+(-0.26)2 +0.042 )/4=2.972/4=0.743

It is same as for original data.

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