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Understanding Variation
Published in D. B. Owen, Beating Your Competition Through Quality, 2020
The mean tells us a great deal, but it does not tell us anything about how the salaries vary. One such measure of variability is the range, which is defined as the difference between the largest salary and the smallest salary. In this case the range is $71,000 − $38,900 = $32,100. Another such measure is the standard deviation, which has a much more complicated formula, but which may be obtained on many hand-held calculators without much difficulty. The standard deviation is the square root of the sum of squared deviations from the mean divided by the number of observations (or the number of observations minus one). The symbol for the standard deviation is sigma (σ) for a population and s for a sample. If the salaries listed are just a sample from a larger group of salaries, then the sample standard deviation, s, is equal to $13,965.39. If, on the other hand, the entire population is represented by this group of five salaries, the population standard deviation, sigma, is equal to $12,491.02.
Statistical Methods for Reproducible Data Analysis
Published in Asis Kumar Tripathy, Chiranji Lal Chowdhary, Mahasweta Sarkar, Sanjaya Kumar Panda, Cognitive Computing Using Green Technologies, 2021
Sambit Kumar Mishra, Mehul Pradhan, Rani Aiswarya Pattnaik
Variance: It is the average squared deviation from the mean. The most important thing to notice is that if we add a constant to each value in the data set, it does not change the distance between values, so the variance remains the same. σ2=∑(x−μ)2n
Statistical and Probabilistic Models
Published in William P. Fox, Robert E. Burks, Modeling Change and Uncertainty, 2022
William P. Fox, Robert E. Burks
Measures of variation or measures of the spread of the data include the variance and standard deviation. They measure the spread in the data, how far the data are from the mean. Variance is simply a measure of the dispersion of a set of data points around their mean value. Variance is a mathematical expectation of the average squared deviations from the mean.
A parametric study on the dynamic ultimate strength of a stiffened panel subjected to wave- and whipping-induced stresses
Published in Ships and Offshore Structures, 2021
George Jagite, Fabien Bigot, Quentin Derbanne, Šime Malenica, Hervé Le Sourne, Patrice Cartraud
Figures 12 and 13 are presenting the dynamic load factors obtained for the wave load and wave+whipping load scenarios, respectively. For each whipping period, six different wave periods have been used. Hence, in order to simplify the representation of the results, the dynamic load factors obtained for wave+whipping scenarios are presented as the mean value, shown as a solid line, and the standard deviation of the results, shown as the shaded area. The mean value is simply the sum of the results divided by the number of elements (i.e. ). While the standard deviation is the square root of the average of the squared deviations from the mean (i.e. ).