A Python function that uses Chauvenet's Criterion to filter outliers from a dataset and returns only the reasonable values.

filter_outliers_chauvenet.py

import numpy
from scipy.special import erfc

def filter_outliers(datapoints):
    """Run Chauvenet's Criterion to remove outliers
    @See: https://www.statisticshowto.com/chauvenets-criterion/
    @See: https://github.com/msproteomicstools/msproteomicstools/blob/master/msproteomicstoolslib/math/chauvenet.py

    Args:
        datapoints (list): Array of datapoints from which to filter the outliers

    Returns:
        list: Valid datapoints with outliers removed
    """
    criterion = 1.0/(2*len(datapoints))
    valid_datapoints = []

    # Step 1: Determine sample mean
    mean = numpy.mean(datapoints)

    # Step 2: Calculate standard deviation of sample
    standard_deviation = numpy.std(datapoints)

    # Step 3: For each value, calculate distance to mean in standard deviations
    # Compare to criterion and store those that pass in valid_periods array
    for datapoint in datapoints:
        distance = abs(datapoint-mean)/standard_deviation  # Distance of a value to mean in stdv's
        distance /= 2.0**0.5                               # The left and right tail threshold values
        probability = erfc(distance)                       # Area normal distribution
        if probability >= criterion:
            valid_datapoints.append(datapoint)             # Store only non-outliers
    
    return valid_datapoints
  
  
# Let's use the function to filter some outliers from a list
mylist = [745, 801, 129876, 793, 698]
valid_list = filter_outliers(mylist)
print(valid_list)