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

Answer:

$\bar{x} = 115.74$

Step-by-step explanation:

We are given the following sample in the question:

115.8, 116.5, 116.1, 115.5, 114.8

Formula:

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

$\bar{x} =\displaystyle\frac{578.7}{5} = 115.74$

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 =

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