Population measurement, such as weight, has calculated numbers {statistic, population}, such as median, mode, mean, and range.
Standard deviation divided by mean {coefficient of variation} {coefficient of variability} {variation coefficient} can measure population variation.
Sum from i = 1 to i = N of n(i) /N, where N equals number of numbers, and n(i) equals number, is a statistic {mean, population}| {average}. For example, the numbers 1, 2, 2, 3, 4, 5, and 6 have mean equal to (1 + 2 + 2 + 3 + 4 + 5 + 6) / 7. Average is number-group balance point, because sum of differences between numbers and mean equals zero.
If numbers are in sequence, middle number of odd number of numbers, or average of two middle numbers of even number of numbers, is a statistic {median, population}|. For example, the numbers 1, 2, 2, 3, 4, 5, and 6 have median equal 3.
Number with greatest frequency is a statistic {mode, population}|. For example, the numbers 1, 2, 2, 4, 5, and 6 have mode equal 2.
Difference between lowest and highest number is a statistic {range, number}. For example, the numbers 1, 2, 2, 3, 4, 5, and 6 have range equal 5.
Mean can divide into quotient error {relative error, statistics}.
Number sets have variance spread {dispersion, statistics}|. Dispersion is torques of numbers around balance point: sum from i = 1 to i = N of (n(i) - x)^2 / N, or sum from i = 1 to i = N of (n(i))^2 / N - x^2, where n(i) are numbers, and x equals mean.
Fourth moment {kurtosis, distribution} measures distribution fatness or slimness.
Square root of mean of squares of differences between numbers and mean {root mean square} (RMS) can equal standard deviation.
Third moment {skewness, distribution} measures distribution asymmetry, whether it is more to right or left of mean. Skew distribution is not symmetric. To find skewness, calculate median and compare to mean.
Sample-mean distribution standard deviation {standard error of the mean}| is smaller than population standard deviation: s / N^0.5, where s is population standard deviation, and N is sample size.
Variance has a square root {standard deviation}|.
Torques of numbers around balance point measure dispersion {variance, distribution}|: sum from i = 1 to i = N of (n(i) - x)^2 / N, or sum from i = 1 to i = N of (n(i))^2 / N - x^2, where n(i) are numbers, and x equals mean.
3-Statistics-Statistical Population
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Date Modified: 2022.0225