Statistics
Descriptive statistics functions
Summary↑
correlation(x, y) | Calculate the the Pearson product-moment correlation coefficient of two lists |
covariance(x, y) | Calculate the covariance of two lists |
geometric_mean(list) | Calculate the geometric mean of a list |
harmonic_mean(list) | Calculates the harmonic mean from a list |
iqr(list) | Calculate the inter-quartile range |
kurtosis(list) | Computes the kurtosis (Fisher) of a list |
max(list) | Get the maximum value from a list |
mean(list) | Calculate the mean from a list of numbers |
median(list) | Get the median value from a list |
median(list, bool2) | |
min(list) | Get the minimum value from a list |
mode(list) | Get the most frequently occuring value |
moment(list, n \\ 1) | Calculates the nth moment about the mean for a sample |
percentile(list, n) | Get the nth percentile cutoff from a list |
quartile(list, atom2) | Get the quartile cutoff value from a list |
range(list) | Get range of data |
skew(list) | Computes the skewness of a data set |
stdev(list) | Calculate the standard deviation of a list |
sum(list) | Sum the contents of a list |
trimmed_mean(list, cutoff) | Calculate the trimmed mean of a list |
variance(list) | Calculate variance from a list of numbers |
zscore(list) | Calculate a standard |
Functions
Calculate the the Pearson product-moment correlation coefficient of two lists.
The two lists are presumed to represent matched pairs of observations, the x
and y
of a simple regression.
Examples
iex> Statistics.correlation([1,2,3,4], [1,3,5,6])
0.9897782665572894
Calculate the covariance of two lists.
Covariance is a measure of how much two random variables change together.
The two lists are presumed to represent matched pairs of observations, such as the x
and y
of a simple regression.
Examples
iex> Statistics.covariance([1,2,3,2,1], [1,4,5.2,7,99])
-17.89
Calculate the geometric mean of a list
Geometric mean is the nth root of the product of n values
Examples
iex> Statistics.geometric_mean([])
nil
iex> Statistics.geometric_mean([1,2,3])
1.8171205928321397
Calculates the harmonic mean from a list
Harmonic mean is the number of values divided by the sum of the reciprocal of all the values.
Examples
iex> Statistics.harmonic_mean([])
nil
iex> Statistics.harmonic_mean([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15])
4.5204836768674568
Calculate the inter-quartile range
Examples
iex> Statistics.iqr([])
nil
iex> Statistics.iqr([1,2,3,4,5,6,7,8,9])
4
Computes the kurtosis (Fisher) of a list.
Kurtosis is the fourth central moment divided by the square of the variance.
Examples
iex> Statistics.kurtosis([])
nil
iex> Statistics.kurtosis([1,2,3,2,1])
-1.1530612244897964
Get the maximum value from a list
iex> Statistics.max([])
nil
iex> Statistics.max([1,2,3])
3
If a non-empty list is provided, it is a call to Enum.max/1
Calculate the mean from a list of numbers
Examples
iex> Statistics.mean([])
nil
iex> Statistics.mean([1,2,3])
2.0
Get the median value from a list.
Pass in true
as a 2nd parameter if you know your list to be already sorted.
Examples
iex> Statistics.median([])
nil
iex> Statistics.median([1,2,3])
2
iex> Statistics.median([1,2,3,4])
2.5
Get the minimum value from a list
iex> Statistics.min([])
nil
iex> Statistics.min([1,2,3])
1
If a non-empty list is provided, it is a call to Enum.min/1
Get the most frequently occuring value
Examples
iex> Statistics.mode([])
nil
iex> Statistics.mode([1,2,3,2,4,5,2,6,7,2,8,9])
2
Calculates the nth moment about the mean for a sample.
Generally used to calculate coefficients of skewness and kurtosis. Returns the n-th central moment as a float The denominator for the moment calculation is the number of observations, no degrees of freedom correction is done.
Examples
iex> Statistics.moment([1,2,3,4,5,6,7,8,9,8,7,6,5,4,3],3)
-1.3440000000000025
iex> Statistics.moment([], 2)
nil
Get the nth percentile cutoff from a list
Examples
iex> Statistics.percentile([], 50)
nil
iex> Statistics.percentile([1,2,3,4,5,6,7,8,9],80)
7.4
iex> Statistics.percentile([1,2,3,4,5,6,7,8,9],100)
9
Get the quartile cutoff value from a list
responds to only first and third quartile.
Examples
iex> Statistics.quartile([1,2,3,4,5,6,7,8,9],:first)
3
iex> Statistics.quartile([1,2,3,4,5,6,7,8,9],:third)
7
Get range of data
Examples
iex> Statistics.range([1,2,3,4,5,6])
5
Computes the skewness of a data set.
For normally distributed data, the skewness should be about 0. A skewness value > 0 means that there is more weight in the left tail of the distribution.
Examples
iex> Statistics.skew([])
nil
iex> Statistics.skew([1,2,3,2,1])
0.3436215967445454
Calculate the standard deviation of a list
Examples
iex> Statistics.stdev([])
nil
iex> Statistics.stdev([1,2])
0.5
Sum the contents of a list
Calls Enum.sum/1
Calculate the trimmed mean of a list.
Can specify cutoff values as a tuple, or simply choose the IQR min/max as the cutoffs
Examples
iex> Statistics.trimmed_mean([], :iqr)
nil
iex> Statistics.trimmed_mean([1,2,3], {1,3})
2.0
iex> Statistics.trimmed_mean([1,2,3,4,5,5,6,6,7,7,8,8,10,11,12,13,14,15], :iqr)
7.3
Calculate variance from a list of numbers
Examples
iex> Statistics.variance([])
nil
iex> Statistics.variance([1,2,3,4])
1.25
iex> Statistics.variance([55,56,60,65,54,51,39])
56.48979591836735
Calculate a standard z
score for each item in a list
Examples
iex> Statistics.zscore([3,2,3,4,5,6,5,4,3])
[-0.7427813527082074, -1.5784103745049407, -0.7427813527082074,
0.09284766908852597, 0.9284766908852594, 1.7641057126819928,
0.9284766908852594, 0.09284766908852597, -0.7427813527082074]