# Descriptive Statistics Calculator

Enter your numerical data below. Separate numbers with either commas or spaces.

Basic Data
Number of Data Points
Sum
Minimum
Maximum
Range
Mean
Truncated Mean 1
Median
Mode(s)
Mode Frequency
Population Variance
Sample Variance
Population Stan. Dev.
Sample Stan. Dev.
Avg. Absolute Dev. 2
Mean Absolute Dev. 3
Median Absolute Dev. 4
Geometric Mean
Harmonic Mean
Interquartile Mean 6
Interquartile Range 7
Trimean 8
Skewness 9
Gini Coefficient 10

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, (∑|xi - 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, (∑|xi - 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{|xi - 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.