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.
116.8 115.7 114.9 115.4 115.9

Required:
a. Calculate the deviations from the mean.
b. Use the deviations calculated in part (a) to obtain the sample variance (in GPa2).

Answer 1

Answer:

a) The deviations from the mean

|x-x⁻|  :   1.06       |-0.04 |       |-0.84 |     |-0.34 |     | 0.16  |  

b)

The variance of the sample      S² = 0.493

The standard deviation of the sample  S =√0.493 = 0.7021

Step-by-step explanation:

Step(i):-

Given that the sample observations

   x   :    116.8       115.7     114.9     115.4     115.9

Mean of the sample

                       = ∑ x/n

 Mean of sample x⁻  = $\frac{116.8+115.7+114.9+115.4+115.9}{5}$

 Mean of sample x⁻ = 115.74        

Step(ii):-    

The deviations from the mean

|x-x⁻|  :  116.8-115.74       115.7-115.74   114.9-115.74  115.4-115.74   115.9-115.74

|x-x⁻|  :   1.06                 |-0.04 |               |-0.84 |         |-0.34 |             | 0.16  |  

|x-x⁻||²:    1.1236             0.0016             0.7056          0.1156             0.0256

The variance of the given sample observations

          S²  = ∑ (x-x⁻)² / n-1

         $S^{2} = \frac{1.1236+0.0016+0.7056+0.1156+0.0256}{5-1} = 0.493$

The variance of the sample      S² = 0.493

The standard deviation of the sample  S =√0.493 = 0.7021