Python statistics | median()

Python is a very popular language when it comes to data analysis and statistics. Luckily, Python3 provide statistics module, which comes with very useful functions like mean(), median(), mode() etc.

median() function in the statistics module can be used to calculate median value from an unsorted data-list. The biggest advantage of using median() function is that the data-list does not need to be sorted before being sent as parameter to the median() function.

Median is the value that separates the higher half of a data sample or probability distribution from the lower half. For a dataset, it may be thought as the middle value. The median is the measure of central tendency of the properties of a data-set in statistics and probability theory. Median has a very big advantage over Mean, which is the median value is not skewed so much by extremely large or small values. The median value is either contained in the data-set of values provided or it doesn’t sway too much from the data provided.



For odd set of elements, the median value is the middle one.
For even set of elements, the median value is the mean of two middle elements.

Median can be represented by the following formula :

   {\displaystyle \mathrm {median} (a)={\frac {a_{\lfloor \#x\div 2\rfloor }+a_{\lfloor \#x\div 2+0.5\rfloor }}{2}}}  

 

Syntax : median( [data-set] )

Parameters :
[data-set] : List or tuple or an iterable with a set of numeric values

Returns : Return the median (middle value) of the iterable containing the data

Exceptions : StatisticsError is raised when iterable passed is empty or when list is null.

Code #1 : Working

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# Python code to demonstrate the  
# working of median() function.
  
# importing statistics module
import statistics
  
# unsorted list of random integers
data1 = [2, -2, 3, 6, 9, 4, 5, -1]
  
  
# Printing median of the
# random data-set
print("Median of data-set is : % s "
        % (statistics.median(data1)))

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Output :

Median of data-set is : 3.5 

 
Code #2 :

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# Python code to demonstrate the
# working of median() on various
# range of data-sets
  
# importing the statistics module
from statistics import median
  
# Importing fractions module as fr
from fractions import Fraction as fr
  
# tuple of positive integer numbers
data1 = (2, 3, 4, 5, 7, 9, 11)
  
# tuple of floating point values
data2 = (2.4, 5.1, 6.7, 8.9)
  
# tuple of fractional numbers
data3 = (fr(1, 2), fr(44, 12),
         fr(10, 3), fr(2, 3))
  
# tuple of a set of  negative integers
data4 = (-5, -1, -12, -19, -3)
  
# tuple of set of positive 
# and negative integers
data5 = (-1, -2, -3, -4, 4, 3, 2, 1)
  
# Printing the median of above datsets
print("Median of data-set 1 is % s" % (median(data1)))
print("Median of data-set 2 is % s" % (median(data2)))
print("Median of data-set 3 is % s" % (median(data3)))
print("Median of data-set 4 is % s" % (median(data4)))
print("Median of data-set 5 is % s" % (median(data5)))

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Output :

Median of data-set 1 is 5
Median of data-set 2 is 5.9
Median of data-set 3 is 2
Median of data-set 4 is -5
Median of data-set 5 is 0.0

 
Code #3 : Demonstrating StatisticsError

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# Python code to demonstrate
# StatisticsError of median()
  
# importing the statistics module
from statistics import median
  
# creating an empty data-set
empty = []
  
# will raise StatisticsError
print(median(empty))

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Output :

Traceback (most recent call last):
  File "/home/3c98774036f97845ee9f65f6d3571e49.py", line 12, in 
    print(median(empty))
  File "/usr/lib/python3.5/statistics.py", line 353, in median
    raise StatisticsError("no median for empty data")
statistics.StatisticsError: no median for empty data

 
Applications :
For practical applications, different measures of dispersion and population tendency are compared on basis how well the corresponding population values can be estimated. For example, a comparison shows that sample mean is more statistically efficient than the sample median when the data is uncontaminated by data from heavily-tailed data distribution or from mixtures of data distribution, but less efficient otherwise and that the efficiency of the sample median is higher than that for a wide range of distributions. To be more specific, the median has 64% efficiency compared to minimum-variance-mean ( for large normal samples ).



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