Question

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

(a) the average hardness value and
(b) the standard deviation hardness value.

46.5 46.9 49.4 50.3 49.8 48.8 47.0 47.7 48.3 49.4 47.8 49.0

Answer 1

a) 48.408

b) 1.235

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{(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{(16.7692)/(12-1) }`

`s=\sqrt{(16.7692)/(11) }`

`s=√(1.5245)`

`s=1.2347`

s=1.235 (rounded to 3 decimal places)

The standard deviation hardness value is 1.235.