[][carthage] [][cocoadocs] [][cocoadocs] [][cocoadocs] [cocoadocs]: http:https://cocoadocs.org/docsets/SigmaSwiftStatistics [carthage]: https://github.com/Carthage/Carthage

This library is a collection of functions that perform statistical calculations in Swift.

• average
• covariancePopulation
• covarianceSample
• max
• median
• medianLow
• medianHigh
• min
• pearson
• standardDeviationPopulation
• standardDeviationSample
• sum
• variancePopulation
• varianceSample

There are three ways you can add Sigma to your Xcode project.

Add source (iOS 7+)

Simply add Sigma.swift file to your project.

Setup with Carthage (iOS 8+)

Alternatively, add github "evgenyneu/SigmaSwiftStatistics" ~> 1.1 to your Cartfile and run carthage update.

Setup with CocoaPods (iOS 8+)

If you are using CocoaPods add this text to your Podfile and run pod install.

use_frameworks!
pod 'SigmaSwiftStatistics', '~> 1.1'

Here is how to use the library in a WatchKit extension with CocoaPods.

use_frameworks!

target 'YourWatchApp Extension Target Name' do
  platform :watchos, '2.0'
  pod 'SigmaSwiftStatistics', '~> 1.1'
end

Add import SigmaSwiftStatistics to your source code if you used Carthage or CocoaPods setup methods.

Returns the maximum value in the array.

Note: returns nil for an empty array.

Sigma.max([1, 8, 3])
// Result: 8

Returns the minimum value in the array.

Note: returns nil for an empty array.

Sigma.min([7, 2, 3])
// Result: 2

Computes sum of values from the array.

Sigma.sum([1, 3, 8])
// Result: 12

Computes arithmetic mean of values in the array.

Note:

• Returns nil for an empty array.
• Same as AVERAGE in Microsoft Excel and Google Docs Sheets.

A = Σ(x) / n

Where:

• n is the number of values.

Sigma.average([1, 3, 8])
// Result: 4

Returns the median value from the array.

Note:

• Returns nil when the array is empty.
• Returns the mean of the two middle values if there is an even number of items in the array.
• Same as MEDIAN in Microsoft Excel and Google Docs Sheets.

Sigma.median([1, 12, 19.5, 3, -5])
// Result: 3

Returns the median value from the array.

Note:

• Returns nil when the array is empty.
• Returns the lower of the two middle values if there is an even number of items in the array.

Sigma.median([1, 12, 19.5, 10, 3, -5])
// Result: 3

Returns the median value from the array.

Note:

• Returns nil when the array is empty.
• Returns the higher of the two middle values if there is an even number of items in the array.

Sigma.median([1, 12, 19.5, 10, 3, -5])
// Result: 10

Computes variance based on a sample.

Note:

• Returns nil when the array is empty or contains a single value.
• Same as VAR, VAR.S or VARA in Microsoft Excel and VAR or VARA in Google Docs Sheets.

s^2 = Σ( (x - m)^2 ) / (n - 1)

Where:

• m is the sample mean.
• n is the sample size.

Sigma.varianceSample([1, 12, 19.5, -5, 3, 8])
// Result: 75.24166667

Computes variance of entire population.

Note:

• Returns nil when the array is empty.
• Same as VAR.P or VARPA in Microsoft Excel and VARP or VARPA in Google Docs Sheets.

σ^2 = Σ( (x - m)^2 ) / n

Where:

• m is the population mean.
• n is the population size.

Sigma.variancePopulation([1, 12, 19.5, -5, 3, 8])
// Result: 62.70138889

Computes standard deviation based on a sample.

Note:

• Returns nil when the array is empty or contains a single value.
• Same as STDEV and STDEV.S in Microsoft Excel and STDEV in Google Docs Sheets.

s = sqrt( Σ( (x - m)^2 ) / (n - 1) )

Where:

• m is the sample mean.
• n is the sample size.

Sigma.standardDeviationSample([1, 12, 19.5, -5, 3, 8])
// Result: 8.674195447801869

Computes standard deviation of entire population.

Note:

• Returns nil for an empty array.
• Same as STDEVP and STDEV.P in Microsoft Excel and STDEVP in Google Docs Sheets.

σ = sqrt( Σ( (x - m)^2 ) / n )

Where:

• m is the population mean.
• n is the population size.

Sigma.standardDeviationPopulation([1, 12, 19.5, -5, 3, 8])
// Result: 7.918420858282849

Computes sample covariance between two variables: x and y.

Note:

• Returns nil if arrays x and y have different number of values.
• Returns nil for empty arrays or arrays containing a single element.
• Same as COVARIANCE.S function in Microsoft Excel.

cov(x,y) = Σ(x - mx)(y - my) / (n - 1)

Where:

• mx is the sample mean of the first variable.
• my is the sample mean of the second variable.
• n is the total number of values.

let x = [1, 2, 3.5, 3.7, 8, 12]
let y = [0.5, 1, 2.1, 3.4, 3.4, 4]
Sigma.covarianceSample(x: x, y: y)
// Result: 5.03

Computes covariance of the entire population between two variables: x and y.

Note:

• Returns nil if arrays x and y have different number of values.
• Returns nil for empty arrays.
• Same as COVAR and COVARIANCE.P functions in Microsoft Excel and COVAR in Google Docs Sheets.

cov(x,y) = Σ(x - mx)(y - my) / n

Where:

• mx is the population mean of the first variable.
• my is the population mean of the second variable.
• n is the total number of values.

let x = [1, 2, 3.5, 3.7, 8, 12]
let y = [0.5, 1, 2.1, 3.4, 3.4, 4]
Sigma.covariancePopulation(x: x, y: y)
// Result: 4.19166666666667

Calculates the Pearson product-moment correlation coefficient between two variables: x and y.

Note:

• Returns nil if arrays x and y have different number of values.
• Returns nil for empty arrays.
• Same as CORREL and PERSON functions in Microsoft Excel and Google Docs Sheets.

p(x,y) = cov(x,y) / (σx * σy)

Where:

• cov is the population covariance.
• σ is the population standard deviation.

let x = [1, 2, 3.5, 3.7, 8, 12]
let y = [0.5, 1, 2.1, 3.4, 3.4, 4]
Sigma.pearson(x: x, y: y)
// Result: 0.843760859352745

You can type a sigma letter σ instead of Sigma. For example:

σ.average([1, 2])
σ.standardDeviationSample([1, 12, 19.5, -5, 3, 8])

If you need help or want to extend the library feel free to create an issue or submit a pull request.

• Thomas Fankhauser
• John Clema

Sigma is released under the MIT License.