Descriptive Statistics Calculator

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¹ To calculate the truncated mean of a set of n data points, first discard the maximum and minimum values, sum the remaining values, then divide by n - 2.

² The Average Absolute Deviation is the mean of the absolute deviations from the median, that is, (∑|x_i - m|)/n, where m is the median and n is the number of points.

³ The Mean Absolute Deviation is the mean of the absolute deviations from the mean, that is, (∑|x_i - x|)/n, where x is the mean and n is the number of points.

⁴ The Median Absolute Deviation is the median of the absolute deviations from the median, that is, MEDIAN{|x_i - m|}, where m is the median.

⁵ The Quadratic Mean is another name for the Root Mean Square. It is calculated by averaging the squared values of the data points, then taking the square root.

⁶ The interquartile mean is the mean of the middle 50% of the data points, that is, you discard the top 25% and bottom 25% of data points. For a set of n data points, the top 25% consists of the top _⌊(n+1)/4_⌋ numbers, where _{⌊ ⌋} is the floor function. Likewise the bottom 25% also consists of _⌊(n+1)/4_⌋ points. Thus, the middle 50% consists of n - 2_⌊(n+1)/4_⌋ numbers.

⁷ The interquartile range is the range of the middle 50% of the data points.

⁸ The TriMean is (Q₁ + 2m + Q₃)/4, where Q₁ is the upper endpoint of the first quartile, m is the median, and Q₃ is the lower end of the third quartile. For a set of n points ordered ascending, Q₁ is the point in position number _⌊(n+1)/4_⌋ + 1. Q₃ is the point in position number n - _⌊(n+1)/4_⌋.

⁹ Skewness measures the tendency of the data to skew to the left or right. Negative skew values indicate more data on the right; positive values indicate more data on the left.

¹⁰ Read Gini Coefficient Calculator for explanation of the Gini coefficient and measures of income equality. The Gini coefficient is only defined for non-negative data.

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