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Computing Summary Statistics (mean, median, standard deviation) using SciPy

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by aryaman@openweaver.com dot icon Updated: Mar 27, 2023

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SciPy is a free and open-source Python library used for scientific computing and technical computing. It is a collection of mathematical algorithms and convenience functions built on the NumPy extension of Python. It adds significant power to the interactive Python session by providing the user with high-level commands and classes for manipulating and visualizing data.

Code

In this solution, we use the lognorm function of the Scipy library

Distribution mean and standard deviation using scipy.stats

PythondotLines of Code : 42dotLicense : Strong Copyleft (CC BY-SA 4.0)

Dependent Libraries : 
>>> import numpy as np
>>> from scipy.stats import lognorm
>>> mu = 0.4104857306
>>> sigma = 3.4070874277012617
>>> lognorm.mean(sigma, 0.0, np.exp(mu))
500.0000010889041

>>> lognorm.mean(sigma, scale=np.exp(mu))
500.0000010889041

>>> lognorm.std(sigma, scale=np.exp(mu))
165831.2402402415

>>> samples = lognorm.rvs(sigma, scale=np.exp(mu), size=10**6)
>>> np.log(samples).mean()  # should be close to mu
0.4134644116056518
>>> np.log(samples).std(ddof=1)  # should be close to sigma
3.4050012251732285

sigma = 0.9444564779275075
mu = 5.768609079062494

>>> from scipy.stats import lognorm
>>> import numpy as np
>>> sigma = 0.9444564779275075
>>> mu = 5.768609079062494
>>> lognorm.mean(sigma, scale=np.exp(mu))
499.9999999949592
>>> lognorm.std(sigma, scale=np.exp(mu))
599.9999996859631

>>> mean = 500.0
>>> var = 600.0**2
>>> sigma = np.sqrt(np.log1p(var/mean**2))
>>> mu = np.log(mean) - 0.5*sigma*sigma
>>> mu, sigma
(5.768609078769636, 0.9444564782482624)
>>> lognorm.mean(sigma, scale=np.exp(mu))
499.99999999999966
>>> lognorm.std(sigma, scale=np.exp(mu))
599.9999999999995
  1. Copy the code using the "Copy" button above, and paste it in a Python file in your IDE.
  2. Modify the values.
  3. Run the file, check the output in terminal.


I hope you found this useful. I have added the link to dependent libraries, version information in the following sections.

Dependent Libraries


scipyby scipy

Python doticonstar image 11340 doticonVersion:v1.11.0rc1doticon
License: Permissive (BSD-3-Clause)

SciPy library main repository

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            scipyby scipy

            Python doticon star image 11340 doticonVersion:v1.11.0rc1doticon License: Permissive (BSD-3-Clause)

            SciPy library main repository
            Support
              Quality
                Security
                  License
                    Reuse

                      If you do not have Scipy required to run this code, you can install it by clicking on the above link and copying the pip Install command from the Scipy page in Kandi.

                      Environment Tested 

                      I tested this solution in the following versions. Be mindful of changes when working with other versions. 

                      1. The solution is created in Python3.11. 
                      2. The solution is tested on Scipy 1.10 version. 

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