The results of a number of fracture toughness tests on dolomitic limestone are given in Table B.1. Determine the sample values of the mean, standard deviation, and coefficient of variation.

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Accepted Answer

Equations B.1 to B.3

[latex]\bar{x}=\frac{1}{n} \sum_{i=1}^n x_i[/latex] (B.1)

[latex]s_x=\sqrt{\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}}=\sqrt{\frac{\sum_{i=1}^n x_i^2-n \bar{x}^2}{n-1}}[/latex] (B.2)

[latex]\delta_x=\frac{s_x}{\bar{x}}[/latex] (B.3)

are needed, for which n = 11, and the [latex]x_{i}[/latex] are the various [latex]K_{Ic}[/latex] values. Performing these computations gives

[latex]\bar{x}=1.300 MPa \sqrt{ m }, \quad s_x=0.0797 MPa \sqrt{ m }[/latex]

[latex]\delta_x=s_x / \bar{x}=0.0613=6.13 \%[/latex]

Table B.1 Fracture Toughness Data for Dolomitic Limestone
Test No.	$K_{I c}, MPa \sqrt{ m }$	Test No.	$K_{I c}, MPa \sqrt{ m }$
1	1.305	7	1.197
2	1.341	8	1.334
3	1.355	9	1.306
4	1.437	10	1.300
5	1.192	11	1.183
6	1.353
Source: Data from [Karfakis 90].

Question B.1: The results of a number of fracture toughness tests on dolom...

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