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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.
It is the mean divided by the standard deviation of a difference between two random values each from one of two groups. It was initially proposed for quality control [ 1 ] and hit selection [ 2 ] in high-throughput screening (HTS) and has become a statistical parameter measuring effect sizes for the comparison of any two groups with random values.
Excel graph of the difference between two evaluations of the smallest root of a quadratic: direct evaluation using the quadratic formula (accurate at smaller b) and an approximation for widely spaced roots (accurate for larger b). The difference reaches a minimum at the large dots, and round-off causes squiggles in the curves beyond this minimum.
The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean , =. [1] It shows the extent of variability in relation to the mean of the population. The coefficient of variation should be computed only for data measured on scales that have a meaningful zero ( ratio scale ) and hence allow relative comparison of ...
A system of a large number of particles is characterized by the mean values of a relatively few number of macroscopic quantities such as temperature, energy, and density. The standard deviation is an important measure in fluctuation theory, which explains many physical phenomena, including why the sky is blue. [4]
For the variables under examination, analysts typically obtain descriptive statistics for them, such as the mean (average), median, and standard deviation. [61] They may also analyze the distribution of the key variables to see how the individual values cluster around the mean. [62] An illustration of the MECE principle used for data analysis.
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 mean absolute difference is not defined in terms of a specific measure of central tendency, whereas the standard deviation is defined in terms of the deviation from the arithmetic mean. Because the standard deviation squares its differences, it tends to give more weight to larger differences and less weight to smaller differences compared ...