Mathematical Modules in Python: Statistics

Python's statistics module provides powerful data statistical analysis capabilities to help us quickly understand the overall characteristics of data, such as biostatistics and business analysis. Instead of looking at data points one by one, just look at statistics such as mean or variance to discover trends and features in the original data that may be ignored, and compare large datasets more easily and effectively.

This tutorial will explain how to calculate the mean and measure the degree of dispersion of the dataset. Unless otherwise stated, all functions in this module support the calculation of the average value using the mean() function rather than simply summing the average. Floating point numbers can also be used.

import random
import statistics
from fractions import Fraction as F

int_values = [random.randrange(100) for x in range(9)]
frac_values = [F(1, 2), F(1, 3), F(1, 4), F(1, 5), F(1, 6), F(1, 7), F(1, 8), F(1, 9)]

mix_values = [*int_values, *frac_values]

print(statistics.mean(mix_values))
# 929449/42840

print(statistics.fmean(mix_values))
# 21.69582166199813

Starting with Python 3.8, you can use the geometric_mean(data, weights=None) and harmonic_mean(data, weights=None) functions to calculate the geometric mean and the harmonic mean.

The geometric mean is the result of dividing the product of all n values ​​in the data to the root of the n power. Due to floating point errors, the results may be slightly biased in some cases. One application of geometric mean is to quickly calculate the compound annual growth rate. For example, a company's four-year sales are 100, 120, 150, and 200, respectively. The growth rates in three years were 20%, 25% and 33.33% respectively. The average sales growth rate of a company will be more accurately expressed as a geometric average of percentages. The arithmetic mean always gives an incorrect and slightly higher rate of growth.

import statistics

growth_rates = [20, 25, 33.33]

print(statistics.mean(growth_rates))
# 26.11

print(statistics.geometric_mean(growth_rates))
# 25.542796263143476

The harmonic mean is just the reciprocal of the arithmetic mean of the reciprocal of the data. If the data contains zero or negative numbers, a StatisticsError exception is thrown.

The harmonic average is used to calculate the average of ratios and rates, such as calculating the average speed, density, or parallel resistance. The following code calculates the average speed when someone travels a fixed distance (here is 100 km).

import statistics

speeds = [30, 40, 60]
distance = 100

total_distance = len(speeds) * distance
total_time = 0

for speed in speeds:
    total_time += distance / speed

average_speed = total_distance / total_time

print(average_speed)
# 39.99999999999999

print(statistics.harmonic_mean(speeds))
# 40.0

It should be noted that when there are multiple values ​​with the same frequency of occurrence, the multimode() function in Python 3.8 can return multiple results.

import statistics

favorite_pet = ['cat', 'dog', 'dog', 'mouse', 'cat', 'cat', 'turtle', 'dog']

print(statistics.multimode(favorite_pet))
# ['cat', 'dog']

Calculate the median

Calculating the center value with a mode may be misleading. As mentioned earlier, mode is always the most frequent data point, regardless of other values ​​in the dataset. Another way to determine the center position is to use the pvariance(data, mu=None) function to calculate the population variance of a given dataset.

The second parameter of this function is optional. If a value of mu is provided, it should be equal to the mean of the given data. If this value is missing, the mean is calculated automatically. This function is useful when you want to calculate the variance of the entire population. If your data is just a sample of the population, you can use the variance(data, xBar=None) function to calculate the sample variance, where xBar is the mean of a given sample, which is automatically calculated if not provided.

The population standard deviation and sample standard deviation can be calculated using the pstdev(data, mu=None) and stdev(data, xBar=None) functions respectively.

import random
import statistics
from fractions import Fraction as F

int_values = [random.randrange(100) for x in range(9)]
frac_values = [F(1, 2), F(1, 3), F(1, 4), F(1, 5), F(1, 6), F(1, 7), F(1, 8), F(1, 9)]

mix_values = [*int_values, *frac_values]

print(statistics.mean(mix_values))
# 929449/42840

print(statistics.fmean(mix_values))
# 21.69582166199813

As can be seen from the above example, a smaller variance means that more data points are closer to the value of the mean. You can also calculate the standard deviation of decimals and fractions.

Summary

In the last tutorial in this series, we learned the different functions provided in the statistics module. You may have noticed that the data provided to the function is sorted in most cases, but it does not have to be sorted. In this tutorial, I used sorted lists because they make it easier to understand the relationship between the values ​​returned by different functions and the input data.

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