Calculation & Conversion Cheat Sheet

Practical Snippet

Key points: (1) means are sensitive to outliers — in skewed distributions the median and quartiles are the honest summary, and the test is the gap between mean and median; (2) growth must state its base period, use a multiplier (2x) rather than "times growth", and keep comparison periods the same length (7-day and 30-day are not comparable); (3) on small samples (n < 100) percentage uncertainty exceeds the number itself, so 30% may really be 11%–60% and a range beats a point estimate; (4) separate descriptive from inferential statistics — a 95% confidence interval over 30 users is statistically almost meaningless.

// ① 描述统计：偏斜分布用中位数，均值会被极端值拉高
function describe(values) {
  const sorted = [...values].sort((a, b) => a - b)
  const sum = values.reduce((a, b) => a + b, 0)
  const mean = sum / values.length
  const median = sorted.length % 2
    ? sorted[(sorted.length - 1) / 2]
    : (sorted[sorted.length / 2 - 1] + sorted[sorted.length / 2]) / 2
  // 均值与中位数的差距大 ⇒ 分布偏斜 ⇒ 以中位数汇报
  const skewed = Math.abs(mean - median) > Math.abs(median) * 0.1
  return { mean, median, skewed, reported: skewed ? median : mean }
}
console.log(describe([2, 2, 2, 2, 2, 2, 2, 2, 2, 40]))   // skewed: true

// ② 增长：写清基期，用倍数而非「倍增长」
function growth(from, to) {
  return {
    from, to,
    multiple: (to / from).toFixed(2) + 'x',           // 2.00x
    percentChange: (((to - from) / from) * 100).toFixed(1) + '%',
  }
}
console.log(growth(100, 200))    // { multiple: '2.00x', percentChange: '100.0%' }

// ③ 小样本百分比：给区间而不是点估计（Wilson 区间近似）
function wilson(successes, n, z = 1.96) {
  const p = successes / n
  const d = 1 + z * z / n
  const c = (p + z * z / (2 * n)) / d
  const m = z * Math.sqrt((p * (1 - p) + z * z / (4 * n)) / n) / d
  return { low: (c - m), high: (c + m) }
}
const ci = wilson(3, 10)
console.log('3/10 的 95% 区间:', ci.low.toFixed(3), '~', ci.high.toFixed(3))
// 0.112 ~ 0.603  ⇒ 点估计 30% 的不确定性极大

// ④ 同比与环比要保证周期长度一致
function compare(current, previous) {
  return {
    percentChange: (((current - previous) / previous) * 100).toFixed(1) + '%',
    // 🔴 7 日与 30 日不可直接比，必须先归一化
    normalizedDaily: current / 7,
  }
}

// ⑤ 离散程度：标准差 vs 四分位距
function spread(values) {
  const sorted = [...values].sort((a, b) => a - b)
  const q = p => sorted[Math.floor(p * (sorted.length - 1))]
  const iqr = q(0.75) - q(0.25)
  const mean = values.reduce((a, b) => a + b, 0) / values.length
  const sd = Math.sqrt(values.reduce((a, b) => a + (b - mean) ** 2, 0) / values.length)
  return { sd: sd.toFixed(2), iqr, preferIQR: iqr > sd }   // 偏态分布用 IQR