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96 lines
2.9 KiB
Python
96 lines
2.9 KiB
Python
6 years ago
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import math
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from collections import Counter
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from typing import List, Union
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from .friends3 import num_friends
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from ch4.vector import sum_of_squares
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num_points = len(num_friends)
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largest_value = max(num_friends)
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min_value = min(num_friends)
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sorted_values = sorted(num_friends)
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smallest_value = sorted_values[0]
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second_smallest_value = sorted_values[1]
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second_largest_value = sorted_values[-2]
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# Central Tendency
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def mean(seq: List[Union[int, float]]) -> float:
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"""Returns the arithmetic mean of a list of integers."""
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return sum(seq) / len(seq)
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mean_friendships = mean(num_friends)
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def median(seq: List[Union[int, float]]) -> float:
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"""Calculates the median value of a list of integers."""
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sorted_seq = sorted(seq)
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seq_len = len(sorted_seq)
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mid_point_index = seq_len // 2
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if seq_len % 2 == 0: # even case
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return (sorted_seq[mid_point_index] + sorted_seq[mid_point_index + 1]) / 2
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else:
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return sorted_seq[mid_point_index]
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def quantile(seq: List[Union[int, float]], pth: float) -> Union[int, float]:
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"""Returns the pth-percentile value"""
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p_index = int(pth * len(seq))
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sorted_seq = sorted(seq)
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return sorted_seq[p_index]
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def mode(seq: List[Union[int, float]]) -> List[Union[int, float]]:
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"""Returns a list of the most common values."""
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counts = Counter(seq)
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max_value = max(counts.values())
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results = [x_i for x_i, count in counts.items() if count == max_value]
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return sorted(results)
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def data_range(seq: List[Union[int, float]]) -> float:
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"""A measure of data dispersion. The Spread being the difference between
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max and min values.
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Outliers are still a concern withing the provided data.
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"""
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return max(seq) - min(seq)
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def _de_mean(seq: List[Union[int, float]]) -> List[Union[int, float]]:
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"""Translates a sequence of integers by subtracting the mean producing
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a list of deviations from the mean."""
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x_bar = mean(seq)
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return [x_i - x_bar for x_i in seq]
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def variance(seq: List[Union[int, float]]) -> float:
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"""Determines the variance within a data set from the mean. Note
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variance is returned as the square of whatever units were provided.
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If observations were of inches this would return a float value
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in inches squared.
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"""
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assert len(seq) >= 2
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n = len(seq)
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deviations = _de_mean(seq)
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return sum_of_squares(deviations) / (n - 1)
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def standard_deviation(seq: List[Union[int, float]]) -> float:
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"""A measure of dispersion with the same units as the data set.
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Easier to reason about if for example your data set was the
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count of 'Number of friends'.
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Outliers are still a concern withing the provided data.
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"""
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return math.sqrt(variance(seq))
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def interquartile_range(seq: List[Union[int, float]]) -> float:
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"""A more robust measure of dispersion. Is less affected by
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a small number of outliers."""
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return float(quantile(seq, .75) - quantile(seq, .25))
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