Data Organization and Infrastructure Challenges Questions

class StreamingStats:
    def __init__(self):
        self.n = 0           # count
        self.mean = 0.0      # running mean
        self.M2 = 0.0        # sum of squared deviations

    def update(self, x: float) -> None:
        """Ingest a single numeric value."""
        self.n += 1
        delta = x - self.mean
        self.mean += delta / self.n
        delta2 = x - self.mean
        self.M2 += delta * delta2

    def merge(self, other: "StreamingStats") -> None:
        """Merge another StreamingStats into this one (in-place)."""
        if other.n == 0:
            return
        if self.n == 0:
            self.n, self.mean, self.M2 = other.n, other.mean, other.M2
            return
        n1, n2 = self.n, other.n
        delta = other.mean - self.mean
        n = n1 + n2
        # combined mean
        self.mean = (n1 * self.mean + n2 * other.mean) / n
        # combined M2 (parallel algorithm)
        self.M2 = self.M2 + other.M2 + delta * delta * n1 * n2 / n
        self.n = n

    def variance(self, sample: bool = True) -> float:
        """Return sample variance by default; population if sample=False."""
        if self.n < 1:
            return float("nan")
        if sample:
            return self.M2 / (self.n - 1) if self.n > 1 else float("nan")
        else:
            return self.M2 / self.n

    def to_tuple(self):
        """Return (n, mean, M2) for serialization."""
        return (self.n, self.mean, self.M2)