median() function in Python statistics module (original) (raw)

Last Updated : 27 Sep, 2021

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 of as the middle value. The median is the measure of the 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

Python3 `

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)))

`

Output :

Median of data-set is : 3.5

Code #2 :

Python3 `

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 datasets

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)))

`

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

Python3 `

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))

`

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 the basis of how well the corresponding population values can be estimated. For example, a comparison shows that the 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 ).