.. Objectives

.. ----------

.. By the end of this tutorial you will --

.. 1. Get to know simple statistics functions like mean,std etc .. (Remembering)

.. #. Apply them on a real world example. (Applying)

.. Prerequisites

.. -------------

.. Getting started with IPython

.. Loading Data from files

.. Getting started with Lists

.. Author              : Puneeth 

   Internal Reviewer   : Anoop Jacob Thomas<anoop@fossee.in>

   External Reviewer   :

   Checklist OK?       : <put date stamp here, if OK> [2010-10-05]

Hello friends and welcome to the tutorial on Statistics using Python

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In this tutorial, we shall learn

 * Doing simple statistical operations in Python  

 * Applying these to real world problems 

.. #[punch: the prerequisites part may be skipped in the tutorial. It

.. will be provided separately.]

You will need Ipython with pylab running on your computer to use this

tutorial.

Also you will need to know about loading data using loadtxt to be able

to follow the real world application.

.. #[punch: since loadtxt is anyway a pre-req, I would recommend you

.. to use a data file and load data from that. that is good, since you

.. would get to deal with arrays, instead of lists. 

.. Talking of rows and columns of 2-D lists etc is confusing. Also,

.. converting to float can be avoided. The tutorial will feel more

.. natural, is what I think. 

.. The idea of separating the main problem and giving toy examples

.. doesn't sound good. Use the same problem to explain stuff. Or use a

.. smaller data-set or something. Using lists doesn't seem natural.]

We will first start with the most necessary statistical operation i.e

finding mean.

We have a list of ages of a random group of people ::

   age_list = [4,45,23,34,34,38,65,42,32,7]

One way of getting the mean could be getting sum of all the ages and

dividing by the number of people in the group. ::

    sum_age_list = sum(age_list)

sum function gives us the sum of the elements. Note that the

``sum_age_list`` variable is an integer and the number of people or

length of the list is also an integer. We will need to convert one of

them to a float before carrying out the division. ::

    mean_using_sum = float(sum_age_list)/len(age_list)

This obviously gives the mean age but there is a simpler way to do

this in Python - using the mean function::

       mean(age_list)

Mean can be used in more ways in case of 2 dimensional lists.  Take a

two dimensional list ::

     two_dimension=[[1,5,6,8],[1,3,4,5]]

The mean function by default gives the mean of the flattened sequence.

A Flattened sequence means a list obtained by concatenating all the

smaller lists into a large long list. In this case, the list obtained

by writing the two lists one after the other. ::

    mean(two_dimension)

    flattened_seq=[1,5,6,8,1,3,4,5]

    mean(flattened_seq)

As you can see both the results are same. ``mean`` function can also

give us the mean of each column, or the mean of corresponding elements

in the smaller lists. ::

   mean(two_dimension, 0)

   array([ 1. ,  4. ,  5. ,  6.5])

we pass an extra argument 0 in that case.

If we use an argument 1, we obtain the mean along the rows. ::

   mean(two_dimension, 1)

   array([ 5.  ,  3.25])

We can see more option of mean using ::

   mean?

Similarly we can calculate median and stanard deviation of a list

using the functions median and std::

      median(age_list)

      std(age_list)

Median and std can also be calculated for two dimensional arrays along

columns and rows just like mean.

For example ::

       median(two_dimension, 0)

       std(two_dimension, 1)

This gives us the median along the colums and standard devition along

the rows.

Now lets apply this to a real world example 

We will a data file that is at the a path ``/home/fossee/sslc2.txt``.

It contains record of students and their performance in one of the

State Secondary Board Examination. It has 180, 000 lines of record. We

are going to read it and process this data.  We can see the content of

file by double clicking on it. It might take some time to open since

it is quite a large file.  Please don't edit the data.  This file has

a particular structure.

We can do ::

   cat /home/fossee/sslc2.txt

to check the contents of the file.

Each line in the file is a set of 11 fields separated 

by semi-colons Consider a sample line from this file.  

A;015163;JOSEPH RAJ S;083;042;47;00;72;244;;; 

The following are the fields in any given line.

* Region Code which is 'A'

* Roll Number 015163

* Name JOSEPH RAJ S

* Marks of 5 subjects: ** English 083 ** Hindi 042 ** Maths 47 **

Science 35 ** Social 72

* Total marks 244

Now lets try and find the mean of English marks of all students.

For this we do. ::

     L=loadtxt('/home/fossee/sslc2.txt',usecols=(3,),delimiter=';')

     L

     mean(L)

loadtxt function loads data from an external file.Delimiter specifies

the kind of character are the fields of data seperated by. 

usecols specifies  the columns to be used so (3,). The 'comma' is added

because usecols is a sequence.

To get the median marks. ::

    median(L)

Standard deviation. ::

    std(L)

Now lets try and and get the mean for all the subjects ::

     L=loadtxt('/home/fossee/sslc2.txt',usecols=(3,4,5,6,7),delimiter=';')

     mean(L,0)

     array([ 73.55452504,  53.79828941,  62.83342759,  50.69806158,  63.17056881])

As we can see from the result mean(L,0). The resultant sequence  

is the mean marks of all students that gave the exam for the five subjects.

and ::

    mean(L,1)

is the average accumalative marks of individual students. Clearly, mean(L,0)

was a row wise calcultaion while mean(L,1) was a column wise calculation.

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This brings us to the end of the tutorial.

we have learnt

 * How to do the standard statistical operations sum , mean

   median and standard deviation in Python.

 * Combine text loading and the statistical operation to solve

   real world problems.

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This tutorial was created as a part of FOSSEE project, NME ICT, MHRD India

Hope you have enjoyed and found it useful.

Thank you!