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Definitions VII


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Order statistic
The sequence of sample values in ascending order.
Sample median
The middle value in the order statistic associated to a population, or the mean of the two middle values.
Truncated mean / Trimmed mean
A modified sample mean obtained by discarding parts of the sample at the high and low end.
Winsorized mean
A modified sample mean obtained by replacing sample values at the high and low end with the sample value at the boundary of the middle part.
Outlier
An observation that appears to deviate markedly from other members of the sample in which it occurs.
Robust method
A statistical method aimed at not being as badly affected by outliers as the standard procedures.
Hodges–Lehmann estimator
Modified mean obtained by taking the median of the sample containing (x_i+x_j)/2 for all i and j
68.3 %
Estimated ratio of values in the interval "mean plusminus one standard deviation" for a normally distributed sample.
95.4 %
Estimated ratio of values in the interval "mean plusminus two standard deviations" for a normally distributed sample.
99.7 %
Estimated ratio of values in the interval "mean plusminus three standard deviations" for a normally distributed sample.
1.96
Number of standard deviations that define an interval covering an estimated 95% of the values of a normally distributed sample.
Homoscedasticity
The property of a sequence of random variables with the same finite variance.
Margin of error
A term usually defined as the radius of a confidence interval.
Geometric mean
A measure of central tendency obtained by taking the n-th root of the product of n sample values.
Harmonic mean
A measure of central tendency obtained by taking the inverse of the mean of the inverse sample values.
Average of ratios
For which kind of average is the harmonic mean usually appropriate?
Generalized mean / Hölder mean
A measure of central tendency obtained by taking the p-th root of the arithmetic mean of the sample values individually raised to the power of p
Arithmetic mean
Term for the usual mean or average used to distinguish it from the other two Pythagorean means.
Arithmetic mean
Which mean is the greater one in the well-known AM-GM inequality?
Mode
The value that appears most often in a sample
Interquartile Range / IQR / Midspread / Middle Fifty
The difference between the upper and lower quartiles