Question

Below are tabulated a number of Rockwell G hardness values that were measured on a single steel specimen. Compute

Answer 1

Answer:

a) 48.408

b) 1.235

Step-by-step explanation:

a)

The average hardness value xbar can be computed as

xbar=sum of values/number of values

xbar=(46.5+46.9+49.4+50.3+49.8+48.8+47+47.7+48.3+49.4+47.8+49)/12

xbar=580.9/12

xbar=48.408 (rounded to 3 decimal places).

The average hardness value is 48.408.

b)

The standard deviation hardness value s can be computed as

$s=\sqrt{\frac{sum(x-xbar)^2}{n-1} }$

x              x-xbar  (x-xbar) ²

46.5  -1.90833 3.64174

46.9  -1.50833 2.27507

49.4    0.99167 0.98340

50.3     1.89167 3.57840

49.8     1.39167 1.93674

48.8    0.39167 0.15340

47.0           -1.40833 1.98340

47.7   -0.70833 0.50174

48.3           -0.10833 0.01174

49.4    0.99167  0.98340

47.8           -0.60833 0.37007

49.0    0.59167 0.35007

Total                               16.7692

$s=\sqrt{\frac{16.7692}{12-1} }$

$s=\sqrt{\frac{16.7692}{11} }$

$s=\sqrt{1.5245}$

$s=1.2347$

s=1.235 (rounded to 3 decimal places)

The standard deviation hardness value is 1.235.