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Thus the mid-range, which is an unbiased and sufficient estimator of the population mean, is in fact the UMVU: using the sample mean just adds noise based on the uninformative distribution of points within this range. Conversely, for the normal distribution, the sample mean is the UMVU estimator of the mean.
a truncated mean based on data within the interquartile range. Midrange the arithmetic mean of the maximum and minimum values of a data set. Midhinge the arithmetic mean of the first and third quartiles. Quasi-arithmetic mean A generalization of the generalized mean, specified by a continuous injective function. Trimean
For n independent and identically distributed discrete random variables X 1, X 2, ..., X n with cumulative distribution function G(x) and probability mass function g(x) the range of the X i is the range of a sample of size n from a population with distribution function G(x).
Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal N(0,σ 2) Population. In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [1]
In electrical engineering and telecommunications, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower cutoff frequencies. It is usually defined as either the arithmetic mean or the geometric mean of the lower cutoff frequency and the upper cutoff frequency of a band-pass system or a band ...
A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles. The use of the term hinge for the lower or upper quartiles derives from John Tukey 's work on exploratory data analysis in the late 1970s, [ 1 ] and midhinge is a fairly modern term dating from around that time.
However, one may avoid the use of the harmonic mean for the case of "weighting by distance". Pose the problem as finding "slowness" of the trip where "slowness" (in hours per kilometre) is the inverse of speed. When trip slowness is found, invert it so as to find the "true" average trip speed. For each trip segment i, the slowness s i = 1/speed i.