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

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

x              x-xbar  (x-xbar) ²

46.5  -1.908333.64174

46.9  -1.508332.27507

49.4    0.991670.98340

50.3     1.891673.57840

49.8     1.391671.93674

48.8    0.391670.15340

47.0           -1.408331.98340

47.7   -0.708330.50174

48.3           -0.108330.01174

49.4    0.99167  0.98340

47.8           -0.608330.37007

49.0    0.591670.35007

Total                               16.7692

s=1.235 (rounded to 3 decimal places)

The standard deviation hardness value is 1.235.

45

step-by-step explanation:

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step-by-step explanation:

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