You are required to:
(i) Find out what are the sample standard deviation and coefficient of variation of a data set are defined as, and how to calculate these parameters.
(ii) Calculate the mean flexural strength, together with the sample standard deviation and coefficient of variation for the flexural strength data.
(iii) Draw a graph of survival probability Ps against flexural strength, σ. Use the mean rank Ps (survival probability) estimator.
(iv) Draw the corresponding Weibull graph for the material, using the mean rank Ps (survival probability) estimator, and tabulating all the relevant numerical data.
(v) Using the data from (iv), determine the Weibull modulus, m value for the material graphically using least-squares linear regression method to generate the “best-fit” trend- line, giving the regression equation and correlation coefficient R.
Given the number of data, it is recommended that while you check your calculations manually, you use a spreadsheet program such as Excel to tabulate the data, do the calculations, and plot the graphs.
For doing (iv), apart from looking at textbooks on statistics for scientists and engineers, for further information on linear regression and the correlation coefficient R, also look at:
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3-Point Flexural Strength Data for a Ceramic (MPa)