Question

Please answer the below question for all parts. Please show all work and write clearly. Using Minitab and Excel is optional, but if you can please do. Thanks!

1. Injection Molding: Many manufacturing companies in the United States and abroad use molded parts as components of a process. Shrinkage is often a major problem. Thus, a molded die for a part is built larger than nominal size to allow for part shrinkage. In an injection molding study it is known that the shrinkage is influenced by many factors, among which are the injection velocity in ft/sec and mold temperature in C◦. The following data set show the results of a designed experiment in which injection velocity was held at high level and mold temperature was held constant at a low level. The shrinkage is measured in cm × 10⁵.

6.77 6.77 6.83 6.70 6.78 6.70 6.62 6.75

6.66 6.76 6.64 6.76 6.73 6.80 6.72 6.76

6.76 6.68 6.66 6.62 6.72 6.76 6.70 6.78

6.76 6.67 6.70 6.72 6.74 6.81 6.79 6.78

6.66 6.76 6.76 6.78

(a) Find the sample mean (2 decimal places) and sample median (2 decimal places)

(b) Find the sample range (2 decimal places), sample variance (4 decimal places), and sample standard deviation (4 decimal places)

(c) Construct a frequency diagram (frequency histogram) of the data. *Optional*: use Minitab and Excel. *Optional*: (*Attach the hard copy of your Minitab and Excel files).

(d) Construct a relative frequency histogram of the data (*Optional*: use excel) select 6 classes (k=6) and show it here. Is there Skewness of the data? If yes, Skewness to the right or to the left? *Optional*: (*Attach the hard copies of your excel)

(e) Locate and report the first (3 decimal places) and third quartiles (3 decimal places) values. Form a box plot and show it here.

Answer 1

close all,
clear all,
clc,

A = [6.77, 6.77, 6.83, 6.70, 6.78, 6.70, 6.62, 6.75, 6.66, 6.76, 6.64, 6.76, 6.73,...
6.80, 6.72, 6.76, 6.76, 6.68, 6.66, 6.62, 6.72, 6.76, 6.70, 6.78, 6.76, 6.67,...
6.70, 6.72, 6.74, 6.81, 6.79, 6.78, 6.66, 6.76, 6.76, 6.78];

SampleMean = mean(A);
SampleVar = var(A);
SampleSD = std(A);
disp(['Sample Mean = ',num2str(SampleMean)]);
disp(['Sample Range = ',num2str(min(A)),' - ',num2str(max(A))]);
disp(['Sample Variance = ',num2str(SampleVar)]);
disp(['Sample S.D. = ',num2str(SampleSD)]);
hist(A,6);
title('Histogram Plot of Data');

Histogram Plot of Data 12 10 8 6 6.75 6.65 6.7 6.8 6.85

Matlab Output

Sample Mean = 6.73
Sample Range = 6.62 - 6.83
Sample Variance = 0.0029321
Sample S.D. = 0.054149
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