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The median of three vertices in a tree, showing the subtree formed by the union of shortest paths between the vertices. Every tree is a median graph. To see this, observe that in a tree, the union of the three shortest paths between pairs of the three vertices a, b, and c is either itself a path, or a subtree formed by three paths meeting at a single central node with degree three.
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.
It is used to estimate the central location of the univariate data by the calculation of mean, median and mode. [7] Each of these calculations has its own advantages and limitations. The mean has the advantage that its calculation includes each value of the data set, but it is particularly susceptible to the influence of outliers. The median is ...
the weighted arithmetic mean of the median and two quartiles. Winsorized mean an arithmetic mean in which extreme values are replaced by values closer to the median. Any of the above may be applied to each dimension of multi-dimensional data, but the results may not be invariant to rotations of the multi-dimensional space. Geometric median
The median of a symmetric unimodal distribution coincides with the mode. The median of a symmetric distribution which possesses a mean μ also takes the value μ. The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode.
Comparison of mean, median and mode of two log-normal distributions with different skewness. The mode is the point of global maximum of the probability density function. In particular, by solving the equation ( ln f ) ′ = 0 {\displaystyle (\ln f)'=0} , we get that:
The median is the "middle" number of the ordered data set. This means that exactly 50% of the elements are below the median and 50% of the elements are greater than the median. The median of this ordered data set is 70°F. The first quartile value (Q 1 or 25th percentile) is the number that marks one quarter of the ordered data set. In other ...
Violin plots are similar to box plots, except that they also show the probability density of the data at different values, usually smoothed by a kernel density estimator.A violin plot will include all the data that is in a box plot: a marker for the median of the data; a box or marker indicating the interquartile range; and possibly all sample points, if the number of samples is not too high.