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Table of Contents
ND Summary Statistics
The Normal Database (ND) feature in Sift includes a library of summary statistics that the user can choose from.
Here we list all available summary statistics that can be computed against the ND library.
If there is a statistics you wish to calculate but is not included here, email info@has-motion.ca and let us know!
Measures of Central Tendencies
Mean
Definition: The sum of all values divided by the total number of values.
Equation: 
Xi = each score in the dataset
n= sample size
Note: this measure is not a weighted mean or mean of means. If measuring mean of a workspace or library summary level in the Normal Database, the mean is measured across all traces from all trials and workspaces (if Library level summary) in the dataset.
Median
Definition: The value lying at the midpoint of the sorted dataset.
Equation:
- if odd
- if even
- n is the data set/sample size
- X is the ordered list of values in the data set
Mode
Definition: The value that appears most often in a data set.
Trimean
Definition: A weighted average of the median and quartiles of the dataset.
Equation: (quartile1 + median*2 + quartile3)/4
Geometric Mean
Definition: An average of a data set using the product of the values rather than the sum. The nth root of the product of n positive numbers.
Equation: 
Trimmed Mean
Definition: Calculates the mean after removing a percentage of the smallest and largest values in the dataset. In this case, we are using a trimmed mean of 10%
Equation:
Xi = each score in the trimmed data set in ascending order
n= sample size of the trimmed data set
Measures of Dispersion
Standard Deviation
Definition: The square root of the variance of the dataset relative to it's mean.
Equation: 
Xi = each score in the data set
u = mean of the data set
n= sample size of the data set
Variance
Definition: The mean of square differences between each data point and the mean of the data set.
Equation: 
Xi = each score in the data set
u = mean of the data set
n= sample size of the data set
Range
Definition: The size of the narrowest interval that contains all data points in the dataset. Found as the difference between the largest and smallest values in the data set.
Equation: 
X = the data set
Quartiles
Definition: The division of a data set (in ascending order) into four equal portions, each containing 25% of the data points.
Equation: 
N = the number of points in the data set
Interquartile Range
Definition: The range of the middle 50% of the data set. Found by finding the difference between the third quartile (75th percentile) and first quartile (25th percentile).
Equation: 
Percentiles
Definition: The value of a sorted data set where x% of the data is below that value.
Equation: 