Q5 / Is a qualitative control chart suitable for the production process represented by the following data collected during a month? No X1 X2 X3 X4 X5 1 9.92 9.94 9.93 9.95 9.93 2 9.95 9.96 9.96 9.97 9.94 9.98 9.94 9.95 9.97 9.93 4 9.99 9.92 9.93 9.94 9.92 5 9.93 9.95 9.99 9.93 9.94 9.96 9.97 9.94 9.98 9.99 7 9.97 9.94 9.92 9.92 9.93 8 9.94 9.96 9.95 9.96 9.92 9.95 39.93 9.97 9.96 9.98 10 9.96 9.92 9.92 9.94 9.93 Draw the awareness control chart for each of 1- the arithmetic mean 2- the range, knowing that the table for the values of D4, D3, B2, B1, A2 is ,, A2 B1 B2 D3 D4 2 1.880 3.267 3.286 1.023 2.568 2.574 4 0.729 2.266 2.282 5 0.577 2.089 2.114 0.483 0.030 1.970 2.004 7 0.419 0.118 1.882 0.076 1.924 8 0.373 0.185 1.815 0.136 1.864 0.337 0.229 1.761 0.816 1.816 10 0.308 0.284 1.716 0.223 1.777
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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