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The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
In statistical quality control, the ¯ and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. [1] This is connected to traditional statistical quality control (SQC) and statistical process control (SPC).
Figure 2. Box-plot with whiskers from minimum to maximum Figure 3. Same box-plot with whiskers drawn within the 1.5 IQR value. A boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles.
As with the ¯ and s and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [4] Thus, the R chart is examined before the x ¯ {\displaystyle {\bar {x}}} chart; if the R chart indicates the sample variability is in statistical control, then the x ¯ {\displaystyle {\bar {x}}} chart is examined to ...
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The chart portion of the forest plot will be on the right hand side and will indicate the mean difference in effect between the test and control groups in the studies. A more precise rendering of the data shows up in number form in the text of each line, while a somewhat less precise graphic representation shows up in chart form on the right.
The above eight rules apply to a chart of a variable value. A second chart, the moving range chart, can also be used but only with rules 1, 2, 3 and 4. Such a chart plots a graph of the maximum value - minimum value of N adjacent points against the time sample of the range.
Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.