Search results
Results from the WOW.Com Content Network
(The sample mean need not be a consistent estimator for any population mean, because no mean needs to exist for a heavy-tailed distribution.) A well-defined and robust statistic for the central tendency is the sample median, which is consistent and median-unbiased for the population median.
The sampling distribution of a mean is generated by repeated sampling from the same population and recording the sample mean per sample. This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the ...
In statistics, a k-th percentile, also known as percentile score or centile, is a score (e.g., a data point) below which a given percentage k of arranged scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage falls ("inclusive" definition); i.e. a score in the k-th percentile would be above approximately k% of all scores in its set.
The figure illustrates the percentile rank computation and shows how the 0.5 × F term in the formula ensures that the percentile rank reflects a percentage of scores less than the specified score. For example, for the 10 scores shown in the figure, 60% of them are below a score of 4 (five less than 4 and half of the two equal to 4) and 95% are ...
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
Quantiles can be thought of as trimmed maxima or minima: for instance, the 5th percentile is the 5% trimmed minimum. Trimmed estimators used to estimate a location parameter include: Trimmed mean; Modified mean, discarding the minimum and maximum values; Interquartile mean, the 25% trimmed mean; Midhinge, the 25% trimmed mid-range
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...