In a normal distribution, 99.7% of the values are not anomalous. Which means you can throw away 99.7% without losing context. This is useful in sampling.

three_sigma_sampling.py

def sample_anomalous(samples):
    """
    Sampling:
    - Central limit theorem(Alan Turing)
    - 3-sigma rule: In a normal distribution, 99.7% of the values are not anomalous.
        Which means you can throw away 99.7% without losing context.
    - You may also use 2-sigma(95%) or 1-sigma(68%)
    see:
    1. https://youtu.be/inrqE0Grgk0?t=26080 (Emmanuel T Odeke)
    2. https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule
    
    return anomalous spans
    """
    import statistics

    mean = sum(samples) / len(samples)
    stdev = statistics.stdev(samples)
    plus_1_standardDeviations = mean + (1 * stdev)
    minus_1_standardDeviations = mean - (1 * stdev)
    plus_2_standardDeviations = mean + (2 * stdev)
    minus_2_standardDeviations = mean - (2 * stdev)
    plus_3_standardDeviations = mean + (3 * stdev)
    minus_3_standardDeviations = mean - (3 * stdev)

    def one_sigma(samples, plus_1_standardDeviations, minus_1_standardDeviations):
        above = []
        below = []
        nonAnomalous = []
        anomalous = []
        for s in samples:
            if s >= plus_1_standardDeviations:
                above.append(s)
            elif s <= minus_1_standardDeviations:
                below.append(s)
            else:
                nonAnomalous.append(s)
        anomalous = above + below
        return anomalous

    def two_sigma(samples, plus_2_standardDeviations, minus_2_standardDeviations):
        above = []
        below = []
        nonAnomalous = []
        anomalous = []
        for s in samples:
            if s >= plus_2_standardDeviations:
                above.append(s)
            elif s <= minus_2_standardDeviations:
                below.append(s)
            else:
                nonAnomalous.append(s)
        anomalous = above + below
        return anomalous

    def three_sigma(samples, plus_3_standardDeviations, minus_3_standardDeviations):
        above = []
        below = []
        nonAnomalous = []
        anomalous = []
        for s in samples:
            if s >= plus_3_standardDeviations:
                above.append(s)
            elif s <= minus_3_standardDeviations:
                below.append(s)
            else:
                nonAnomalous.append(s)
        anomalous = above + below
        return anomalous

    _one_sigma = one_sigma(samples, plus_1_standardDeviations, minus_1_standardDeviations)
    _two_sigma = two_sigma(samples, plus_2_standardDeviations, minus_2_standardDeviations)
    _three_sigma = three_sigma(samples, plus_3_standardDeviations, minus_3_standardDeviations)
    return _one_sigma, _two_sigma, _three_sigma


latency_samples = [1, 8.5, 9.1, 9.3, 9.4, 9.5, 6.4, 9.7, 9.9, 9.9]
_one_sigma, _two_sigma, _three_sigma = sample_anomalous(latency_samples)
print("_one_sigma, _two_sigma, _three_sigma: ", _one_sigma, _two_sigma, _three_sigma)