# 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 |

Advanced Data | |
---|---|

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 | |

Quadratic Mean ^{5} | |

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.

**The Average Absolute Deviation is the**

^{2}*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.

**The Mean Absolute Deviation is the**

^{3}*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.

**The Median Absolute Deviation is the**

^{4}*median*of the absolute deviations from the

*median*, that is, MEDIAN{|

*x*|}, where

_{i}- m*m*is the median.

**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.**

^{5}**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**

^{6}*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.

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

^{7}**The TriMean is (**

^{8}*Q*

_{1}+ 2

*m*+

*Q*

_{3})/4, where

*Q*

_{1}is the upper endpoint of the first quartile,

*m*is the median, and

*Q*

_{3}is the lower end of the third quartile. For a set of

*n*points ordered ascending,

*Q*

_{1}is the point in position number

_{⌊}(

*n*+1)/4

_{⌋}+ 1.

*Q*

_{3}is the point in position number

*n*-

_{⌊}(

*n*+1)/4

_{⌋}.

**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.**

^{9}**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.**

^{10}© *Had2Know 2010
*