var arr = [1,1,1,2,3,4,5,3,3,3,4,5,6,3,2,4,6];

// first work out the mean
var mean = arr.reduce(function (p, c) {
    return p + c;
}) / arr.length;

// now the stanard deviation
var standardDeviation = Math.sqrt(arr.map(function (l) {
  return Math.pow(l - mean, 2);
}).reduce(function (p, c) {
  return p + c;
}) / arr.length);