Functional Standard Deviation

fstddev.js

// Utilities
const compose = 
  (...fns) => (arg) => fns.reduceRight((composed, func) => func(composed), arg);

const map =
  fn => list => list.map(fn);

const filter =
  predicate => list => list.filter(predicate);

const reduce =
  reducer => list => list.reduce(reducer, []);

const mapReducer =
  fn => (accum, val) => accum.concat(fn(val));

const filterReducer =
  predicate => (accum, val) => (predicate(val) ? accum.concat(val) : accum);

const tap =
  tag => x => (console.log(`${tag}: ${x}`), x);

// Basic Arithmetics
const sumAverage =
  list => list.reduce((sum, x) => x + sum, 0) / list.length;

const exp =
  n => x => Math.pow(x, n);

// Values
const orders = [
  3, 5, 7, 8, 5, 25, 8, 4
];
const average = sumAverage(orders);

/*******************************
 * Stats
 *******************************/
const diff = 
  average => order => order - average;

const sqaredDiffs =
  compose(exp(2), diff(average));

// The variance is the sum of averages of sqared differences
const variance = compose(sumAverage, map(sqaredDiffs));

// The standar deviation is the squared root of the variance
const stdDev =
  compose(Math.sqrt, variance);

const isNotable =
  filterReducer((base => (average, stdv) => elm => elm - average - stdv > base)(0)(average, stdDev(orders)));

// Practical example
// Get the values that stands out
const notables = 
  reduce(isNotable)(orders);

console.log(notables);