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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).
Plot of the standard deviation line (SD line), dashed, and the regression line, solid, for a scatter diagram of 20 points. In statistics , the standard deviation line (or SD line) marks points on a scatter plot that are an equal number of standard deviations away from the average in each dimension.
The second standard deviation from the mean in a normal distribution encompasses a larger portion of the data, covering approximately 95% of the observations. Standard deviation is a widely used measure of the spread or dispersion of a dataset. It quantifies the average amount of variation or deviation of individual data points from the mean of ...
The X-bar chart is always used in conjunction with a variation chart such as the ¯ and R chart or ¯ and s chart. The R-chart shows sample ranges (difference between the largest and the smallest values in the sample), while the s-chart shows the samples' standard deviation. The R-chart was preferred in times when calculations were performed ...
About 68% of values drawn from a normal distribution are within one standard deviation σ from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. [8] This fact is known as the 68–95–99.7 (empirical) rule, or the 3-sigma rule.
Module:Chart creates bar and pie charts on Wikipedia without need for external tools; Many spreadsheet, drawing, and desktop publishing programs allow you to create graphs and export them as images. gnuplot can produce a wide variety of charts and graphs; see samples with source code at Commons. In Python using matplotlib
The geometric standard deviation is used as a measure of log-normal dispersion analogously to the geometric mean. [3] As the log-transform of a log-normal distribution results in a normal distribution, we see that the geometric standard deviation is the exponentiated value of the standard deviation of the log-transformed values, i.e. = ( ()).