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Fifteen Random Samples of Size Four Yield the Following Statistics:Sample Xˉ\bar { X }

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Fifteen random samples of size four yield the following statistics:Sample Xˉ\bar { X } R Sample Xˉ\bar { X } R Sample Xˉ\bar { X } R
1331863334113326233357332131233573335883315133307433779334614330553369103329153346\begin{array} { c c c c c c c c c } 1 & 331 & 8 & 6 & 333 & 4 & 11 & 332 & 6 \\2 & 333 & 5 & 7 & 332 & 13 & 12 & 335 & 7 \\3 & 335 & 8 & 8 & 331 & 5 & 13 & 330 & 7 \\4 & 337 & 7 & 9 & 334 & 6 & 14 & 330 & 5 \\5 & 336 & 9 & 10 & 332 & 9 & 15 & 334 & 6\end{array}
For these data, determine the upper and lower control limits for the Xˉ\bar { X } and R charts.

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Definitions:

Statistical Inference

The process of using data analysis to deduce properties of an underlying probability distribution.

Observational Study

Research where the researcher observes and measures variables without manipulating them, allowing for the study of natural behavior and relationships.

Nominal Scale

A measurement scale used in classifications that involve categorizing data without implying any order or numerical difference between them.

Ratio Scale

A quantitative scale where there is a true zero point and the intervals between different values are meaningful, allowing for the comparison of absolute magnitudes of the numbers.

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