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The median is the value such that the fractions not exceeding it and not falling below it are each at least 1/2. It is not necessarily unique, but never infinite or totally undefined. For a data sample it is the "halfway" value when the list of values is ordered in increasing value, where usually for a list of even length the numerical average ...
The median is 3 and the weighted median is the element corresponding to the weight 0.3, which is 4. The weights on each side of the pivot add up to 0.45 and 0.25, satisfying the general condition that each side be as even as possible. Any other weight would result in a greater difference between each side of the pivot.
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter. The median of a power law distribution x −a, with exponent a > 1 is 2 1/(a − 1) x min, where x min is the minimum value for which the power law holds [10]
The IQR, mean, and standard deviation of a population P can be used in a simple test of whether or not P is normally distributed, or Gaussian. If P is normally distributed, then the standard score of the first quartile, z 1, is −0.67, and the standard score of the third quartile, z 3, is +0.67.
It has a median value of 2. The absolute deviations about 2 are (1, 1, 0, 0, 2, 4, 7) which in turn have a median value of 1 (because the sorted absolute deviations are (0, 0, 1, 1, 2, 4, 7)). So the median absolute deviation for this data is 1.
The bold numbers (36, 39) are used to calculate the median as their average. As there are an even number of data points, the first three methods all give the same results. (The Method 3 is executed such that the median is not chosen as a new data point and the Method 1 started.)
The median of the first group is the lower or first quartile, and is equal to (0 + 1)/2 = 0.5. The median of the second group is the upper or third quartile, and is equal to (27 + 61)/2 = 44. The smallest and largest observations are 0 and 63. So the five-number summary would be 0, 0.5, 7.5, 44, 63.