Page 226 - Materials Science and Engineering An Introduction

198 • Chapter 6 / Mechanical Properties of Metals

where n is the number of observations or measurements and x i is the value of a discrete
measurement.
Furthermore, the standard deviation s is determined using the following expression:

n 1/2
a (x i - x) 2
Computation of £ i=1 §
standard deviation s = (6.22)
n - 1

where x i , x, and n were defined earlier. A large value of the standard deviation corre-
sponds to a high degree of scatter.

EXAMPLE PROBLEM 6.6

Average and Standard Deviation Computations
The following tensile strengths were measured for four specimens of the same steel alloy:

Sample Number Tensile Strength (MPa)
1 520
2 512
3 515
4 522

(a) Compute the average tensile strength.
(b) Determine the standard deviation.

Solution
(a) The average tensile strength (TS) is computed using Equation 6.21 with n = 4:
4
a (TS) i
i=1
TS =
4
520 + 512 + 515 + 522
=
4
= 517 MPa
(b) For the standard deviation, using Equation 6.22, we obtain
4 1/2
a {(TS) i - TS} 2
£ i=1 §
s =
4 - 1
2
2
2
(520 - 517) + (512 - 517) + (515 - 517) + (522 - 517) 2 1/2
= c d
4 - 1
= 4.6 MPa
Figure 6.20 presents the tensile strength by specimen number for this example problem
and also how the data may be represented in graphical form. The tensile strength data
point (Figure 6.20b) corresponds to the average value TS, and scatter is depicted by error