statistics-math.ts

function average(values: number[]): number {
  const sum = values.reduce((acc, current) => acc + current, 0);
  return sum / values.length;
}

export function standardDeviation(values: number[]): number {
  /** https://www.mathsisfun.com/data/standard-deviation-formulas.html
   * 1. Work out the Mean (the simple average of the numbers)
   * 2. Then for each number: subtract the Mean and square the result
   * 3. Then work out the mean of those squared differences.
   * 4. Take the square root of that and we are done! */

  const mean = average(values);
  const squaredDifferences = values.map((value) => Math.pow(value - mean, 2));
  const differenceMean = average(squaredDifferences);
  const result = Math.sqrt(differenceMean);
  return result;
}

export function zScores(values: number[]): number[] {
  // https://statisticsbyjim.com/basics/outliers/
  const mean = average(values);
  const deviation = standardDeviation(values);
  const zScores = values.map((value) => {
    if (deviation === 0) {
      return 0;
    }
    return (value - mean) / deviation;
  });
  return zScores;
}

export function p50(values: number[]): number {
  const p50Index = Math.floor(values.length / 2);
  const smallestToBiggest = [...values].sort((a, b) => a - b);
  return smallestToBiggest[p50Index];
}