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In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...
The sample range is the difference between the maximum and minimum. It is a function of the order statistics: ... Using the above formulas, ... financial mathematics ...
where ¯ ¯ and ¯ are the estimates of the long-term process mean and range established during control-chart setup and A 2, D 3, and D 4 are sample size-specific anti-biasing constants. The anti-biasing constants are typically found in the appendices of textbooks on statistical process control .
If the set is a sample from the whole population, then the unbiased sample variance can be calculated as 1017.538 that is the sum of the squared deviations about the mean of the sample, divided by 11 instead of 12. A function VAR.S in Microsoft Excel gives the unbiased sample variance while VAR.P is for population variance.
There is a paucity of reliable guidance on estimating sample sizes before starting the research, with a range of suggestions given. [ 16 ] [ 19 ] [ 20 ] [ 21 ] In an effort to introduce some structure to the sample size determination process in qualitative research, a tool analogous to quantitative power calculations has been proposed.
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
Sample extrema can be used for normality testing, as events beyond the 3σ range are very rare. The sample extrema can be used for a simple normality test, specifically of kurtosis: one computes the t-statistic of the sample maximum and minimum (subtracts sample mean and divides by the sample standard deviation), and if they are unusually large ...
The sample median is the most examined one amongst quantiles, being an alternative to estimate a location parameter, when the expected value of the distribution does not exist, and hence the sample mean is not a meaningful estimator of a population characteristic. Moreover, the sample median is a more robust estimator than the sample mean.