Question

a) Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations:

116.2

115.8

114.9

115.4

115.5

(a) Calculate x.
= GPa

Calculate the deviations from the mean. (Enter your answers to two decimal places.)

x	116.2	115.8	114.9	115.4	115.5
deviation

(b) Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation. (Round your answers to three decimal places.)

s2	=	GPa2
s	=	GPa

(c) Calculate s² by using the computational formula for the numerator S_xx. (Round your answer to three decimal places.)
= GPa²

(d) Subtract 100 from each observation to obtain a sample of transformed values. Now calculate the sample variance of these transformed values. (Round your answer to three decimal places.)
= GPa²

Compare it to s² for the original data.

The variance in part (d) is greater than the variance in part (b).

The variance in part (d) is equal to the variance in part (b).     

The variance in part (d) is smaller than the variance in part (b)

Answer 1

a)

Sample mean ( )

, where , n is sample is size = 5

Deviations from the mean = x_i -   

b)

sample variance :

Where ,

Calculation :

So, sample variance is ,

sample standard deviation :

c)

Computational formula for Sxx :

Calculation :

,  

So,

So s^2 is,

d)

Subtract 100 from each observation to obtain a sample of transformed values.

Let, transformed values = yi = xi - 100

,    

So, variance of transformed values is ,

The variance in part (d) is equal to the variance in part (b).