Search results
Results from the WOW.Com Content Network
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.
The deviation of each data point is calculated by subtracting the mean of the data set from the individual data point. Mathematically, the deviation d of a data point x in a data set with respect to the mean m is given by the difference: = This calculation represents the "distance" of a data point from the mean and provides information about ...
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] 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.
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
For a set of numbers {10, 15, 30, 45, 57, 52 63, 72, 81, 93, 102, 105}, if this set is the whole data population for some measurement, then variance is the population variance 932.743 as the sum of the squared deviations about the mean of this set, divided by 12 as the number of the set members.
In statistics, pooled variance (also known as combined variance, composite variance, or overall variance, and written ) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Using two points, a simple estimate is the midhinge (the 25% trimmed mid-range), but a more efficient estimate is the 29% trimmed mid-range, that is, averaging the two values 29% of the way in from the smallest and the largest values: the 29th and 71st percentiles; this has an efficiency of about 81%. [3]