Swift Array extension for standard deviation

There's actually a class that provides this functionality already - called NSExpression. You could reduce your code size and complexity by using this instead. There's quite a bit of stuff to this class, but a simple implementation of what you want is as follows.

let expression = NSExpression(forFunction: "stddev:", arguments: [NSExpression(forConstantValue: [1,2,3,4,5])])
let standardDeviation = expression.expressionValueWithObject(nil, context: nil)

You can calculate mean too, and much more. Info here: http://nshipster.com/nsexpression/

Swift 4 Array extension with FloatingPoint elements:

extension Array where Element: FloatingPoint {

    func sum() -> Element {
        return self.reduce(0, +)
    }

    func avg() -> Element {
        return self.sum() / Element(self.count)
    }

    func std() -> Element {
        let mean = self.avg()
        let v = self.reduce(0, { $0 + ($1-mean)*($1-mean) })
        return sqrt(v / (Element(self.count) - 1))
    }

}