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In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
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).
The "chart" actually consists of a pair of charts: One to monitor the process standard deviation (as approximated by the sample moving range) and another to monitor the process mean, as is done with the ¯ and s and individuals control charts.
Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: Standard deviation; Interquartile range (IQR) Range; Mean absolute difference (also known as Gini mean absolute difference)
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 ...
In educational assessment, T-score is a standard score Z shifted and scaled to have a mean of 50 and a standard deviation of 10. [14] [15] [16] In bone density measurements, the T-score is the standard score of the measurement compared to the population of healthy 30-year-old adults, and has the usual mean of 0 and standard deviation of 1. [17]
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Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation, mean absolute difference and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation.