Question

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

115.8 116.5 116.1 115.5 114.8

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

Answer 1

`\bar{x} = 115.74`

Explanation:

We are given the following sample in the question:

115.8, 116.5, 116.1, 115.5, 114.8

Formula:

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`\bar{x} =\displaystyle(578.7)/(5) = 115.74`

Deviations from mean:

`x_i-\bar{x}\\\\115.8 - 115.74 =0.06\\116.5 - 115.74 = 0.76\\116.1 - 115.74 = 0.36\\115.5 - 115.74 = -0.24\\114.8 - 115.74 = -0.94`

Sum of Deviations =

`0.06 + 0.76 + 0.36 - 0.24 - 0.94 = 0`