median of a continuous frequency distribution

bucketMedian.js

const amount = 10000; // the smaller the amount, the more the bucket median is off
const data = generateValues(amount, 300);

console.log({
  amount,
  normalMedian: normalMedian(data.values),
  bucketMedian: bucketMedian(data.buckets),
});

function normalMedian(arr) {
  const arr2 = arr.slice(0).sort((a, b) => a - b);
  const idx = Math.floor(arr2.length / 2);

  // for even numbers (https://www.gstatic.com/education/formulas/images_long_sheet/en/median_formula.svg)
  if (arr2.length % 2 === 0) {
    return (arr2[idx - 1] + arr2[idx]) / 2;
  } else {
    return arr2[idx];
  }
}

// ref: https://www.mathstips.com/median-for-discrete-and-continuous-frequency-type/
function bucketMedian(buckets) {
  const cumulative = [];
  const totalFrequency = buckets.reduce((sum, f, idx) => {
    cumulative[idx] = sum + f;
    return cumulative[idx];
  }, 0);
  const medianBucketIdx = cumulative.findIndex(cf => cf > totalFrequency / 2);
  return Math.round(
    (medianBucketIdx + (totalFrequency / 2 - cumulative[medianBucketIdx - 1]) / buckets[medianBucketIdx]) * 10,
  );
}

function generateValues(amount, range) {
  const values = new Array(amount);
  const buckets = [];
  for (let a = 0; a < amount; a++) {
    const value = Math.floor(Math.random() * range);
    values[a] = value;
    const idx = Math.floor(value / 10);
    buckets[idx] = (buckets[idx] || 0) + 1;
  }

  return { values, buckets };
}