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The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.
Each quartile is a median [8] calculated as follows. Given an even 2n or odd 2n+1 number of values first quartile Q 1 = median of the n smallest values third quartile Q 3 = median of the n largest values [8] The second quartile Q 2 is the same as the ordinary median. [8]
If there are an even number of data points in the original ordered data set, split this data set exactly in half. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data. This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.
In mathematics, the mediant of two fractions, generally made up of four positive integers. and is defined as + +.. That is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively.
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.
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic , being more resilient to outliers in a data set than the standard deviation . In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it.
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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.