--- a/day1/session3.tex Fri Nov 06 17:56:22 2009 +0530
+++ b/day1/session3.tex Fri Nov 06 18:33:08 2009 +0530
@@ -78,6 +78,7 @@
\author[FOSSEE] {FOSSEE}
\institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay}
+
\date[] {7 November, 2009\\Day 1, Session 3}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -126,67 +127,88 @@
%% % You might wish to add the option [pausesections]
%% \end{frame}
+\section{Computing mean}
+\begin{frame}
+ \frametitle{Value of acceleration due to gravity?}
+ \begin{itemize}
+ \item We already have pendulum.txt
+ \item We know that $ T = 2\pi \sqrt{\frac{L}{g}} $
+ \item So $ g = \frac{4 \pi^2 L}{T^2} $
+ \item Calculate ``g'' - acceleration due to gravity for each pair of L and T
+ \item Hence calculate mean ``g''
+ \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Acceleration due to gravity - ``g''\ldots}
+ \begin{lstlisting}
+In []: G = []
+In []: for line in open('pendulum.txt'):
+ .... points = line.split()
+ .... l = float(points[0])
+ .... t = float(points[1])
+ .... g = 4 * pi * pi * l / t * t
+ .... G.append(g)
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Computing mean ``g''}
+ \begin{block}{Exercise}
+ Obtain the mean of ``g''
+ \end{block}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Mean ``g''}
+ \begin{lstlisting}
+total = 0
+for g in G:
+ total += g
+
+mean_g = total / len(g)
+print "Mean: ", mean_g
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Mean ``g''}
+ \begin{lstlisting}
+mean_g = sum(G) / len(G)
+print "Mean: ", mean_g
+ \end{lstlisting}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Mean ``g''}
+ \begin{lstlisting}
+mean_g = mean(G)
+print "Mean: ", mean_g
+ \end{lstlisting}
+ \inctime{10}
+\end{frame}
+
\section{Processing voluminous data}
\begin{frame}
\frametitle{More on data processing}
\begin{block}{}
- We have a huge--1m records--data file.\\How do we do \emph{efficient} statistical computations, that is find mean, median, mode, standard deveiation etc; draw pie charts?
+ We have a huge data file--180,000 records.\\How do we do \emph{efficient} statistical computations, i.e. find mean, median, standard deviation etc; draw pie charts?
\end{block}
\end{frame}
-
-\begin{frame}
- \frametitle{Statistical Analysis: Problem statement}
- Read the data supplied in \emph{sslc1.txt} and carry out the following:
- \begin{enumerate}
- \item Draw a pie chart representing the proportion of students who scored more than 90\% in each region in Science.
- \item Draw a pie chart representing the proportion of students who scored more than 90\% in each subject across regions.
- \item Print mean, median, mode and standard deviation of math scores for all regions combined.
- \end{enumerate}
-\end{frame}
-
-\begin{frame}
- \frametitle{Problem statement: explanation}
- \emphbar{Draw a pie chart representing the proportion of students who scored more than 90\% in each region in Science.}
- \begin{enumerate}
- \item Complete(100\%) data - Number of students who scored more than 90\% in Science
- \item Each slice - Number of students who scored more than 90\% in Science in one region
- \end{enumerate}
-\end{frame}
-
\begin{frame}
- \frametitle{Problem statement: explanation}
- \emphbar{Draw a pie chart representing the proportion of students who scored more than 90\% in each subject across regions.}
- \begin{enumerate}
- \item Complete(100\%) data - Number of students who scored more than 90\% across all regions
- \item Each slice - Number of students who scored more than 90\% in each subject across all regions
- \end{enumerate}
+ \frametitle{Structure of the file}
+ Understanding the structure of sslc1.txt
+ \begin{itemize}
+ \item Each line in the file has a student's details(record)
+ \item Each record consists of fields separated by ';'
+ \end{itemize}
+\emphbar{A;015162;JENIL T P;081;060;77;41;74;333;P;;}
\end{frame}
\begin{frame}
- \frametitle{Statistical Analysis and Parsing \ldots}
- Machinery Required -
- \begin{itemize}
- \item File reading
- \item Parsing
- \item Dictionaries
- \item NumPy arrays
- \item Statistical operations
- \end{itemize}
-\end{frame}
-
-\begin{frame}
- \frametitle{File reading and parsing}
- Understanding the structure of sslc1.txt
- \begin{itemize}
- \item One line in file corresponds to a student's details
- \item aka record
- \item Each record consists of fields separated by ';'
- \end{itemize}
-\end{frame}
-
-\begin{frame}
- \frametitle{File reading and parsing \ldots}
+ \frametitle{Structure of the file \ldots}
+\emphbar{A;015163;JOSEPH RAJ S;083;042;47;AA;72;244;;;}
Each record consists of:
\begin{itemize}
\item Region Code
@@ -195,11 +217,43 @@
\item Marks of 5 subjects: English, Hindi, Maths, Science, Social
\item Total marks
\item Pass/Fail (P/F)
- \item Withdrawn (W)
+ \item Withheld (W)
\end{itemize}
\inctime{5}
\end{frame}
+\begin{frame}
+ \frametitle{Statistical Analysis: Problem statement}
+ 1. Read the data supplied in the file \emph{sslc1.txt} and carry out the following:
+ \begin{itemize}
+ \item[a] Draw a pie chart representing proportion of students who scored more than 90\% in each region in Science.
+ \item[b] Print mean, median and standard deviation of math scores for all regions combined.
+ \end{itemize}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Problem statement: explanation}
+ \emphbar{a. Draw a pie chart representing proportion of students who scored more than 90\% in each region in Science.}
+\begin{columns}
+ \column{5.25\textwidth}
+ \hspace*{.5in}
+\includegraphics[height=2.6in, interpolate=true]{data/science}
+ \column{0.8\textwidth}
+\end{columns}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Machinery Required}
+ \begin{itemize}
+ \item File reading
+ \item Parsing
+ \item Dictionaries
+ \item List enumeration
+ \item Arrays
+ \item Statistical operations
+ \end{itemize}
+\end{frame}
+
\subsection{Data processing}
\begin{frame}[fragile]
\frametitle{File reading and parsing \ldots}
@@ -207,100 +261,71 @@
for record in open('sslc1.txt'):
fields = record.split(';')
\end{lstlisting}
+\begin{block}{}
+\centerline{Recall pendulum example!}
+\end{block}
\end{frame}
-\subsection{Dictionary}
+\subsection{Dictionaries}
\begin{frame}[fragile]
- \frametitle{Dictionary: Introduction}
+ \frametitle{Dictionaries: Introduction}
\begin{itemize}
\item lists index: 0 \ldots n
\item dictionaries index using strings
\end{itemize}
- \begin{block}{Example}
-d = \{ ``Hitchhiker's guide'' : 42,
- ``Terminator'' : ``I'll be back''\}\\
-d[``Terminator''] => ``I'll be back''
- \end{block}
\end{frame}
\begin{frame}[fragile]
- \frametitle{Dictionary: Introduction}
+ \frametitle{Dictionaries \ldots}
\begin{lstlisting}
-In [1]: d = {"Hitchhiker's guide" : 42,
- "Terminator" : "I'll be back"}
+In []: d = {"jpg" : "image file",
+ "txt" : "text file",
+ "py" : "python code"}
-In [2]: d["Hitchhiker's guide"]
-Out[2]: 42
-
-In [3]: "Hitchhiker's guide" in d
-Out[3]: True
-
-In [4]: "Guido" in d
-Out[4]: False
+In []: d["txt"]
+Out[]: 'text file'
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
- \frametitle{Dictionary: Introduction}
+ \frametitle{Dictionaries \ldots}
\begin{lstlisting}
-In [5]: d.keys()
-Out[5]: ['Terminator', "Hitchhiker's
- guide"]
+In []: "py" in d
+Out[]: True
-In [6]: d.values()
-Out[6]: ["I'll be back", 42]
+In []: "cpp" in d
+Out[]: False
\end{lstlisting}
\end{frame}
\begin{frame}[fragile]
- \frametitle{Back to lists: Iterating}
- \begin{itemize}
- \item Python's \kwrd{for} loop iterates through list items
- \item In other languages (C/C++) we run through indices and pick items from the array using these indices
- \item In Python, while iterating through list items current position is not available
- \end{itemize}
- \begin{block}{Iterating through indices}
- What if we want the index of an item of a list?
- \end{block}
+ \frametitle{Dictionaries \ldots}
+ \begin{lstlisting}
+In []: d.keys()
+Out[]: ['py', 'txt', 'jpg']
+In []: d.values()
+Out[]: ['python code', 'text file',
+ 'image file']
+ \end{lstlisting}
+ \inctime{10}
\end{frame}
\begin{frame}[fragile]
- \frametitle{enumerate: Iterating through list indices}
- \begin{lstlisting}
-In [1]: names = ["Guido","Alex", "Tim"]
-
-In [2]: for i, name in enumerate(names):
- ...: print i, name
- ...:
-0 Guido
-1 Alex
-2 Tim
- \end{lstlisting}
- \inctime{5}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Continuing with our Dictionary}
+ \frametitle{Getting back to the problem}
Let our dictionary be:
\begin{lstlisting}
-science = {} # is an empty dictionary
+science = {}
\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Dictionary - Building parsed data}
- \begin{itemize}
- \item \emph{Keys} of \emph{science} will be region codes
- \item Value of a \emph{science} will be the number students who scored more than 90\% in that region
+\begin{itemize}
+ \item Keys will be region codes
+ \item Values will be the number students who scored more than 90\% in that region
\end{itemize}
\end{frame}
\begin{frame}[fragile]
\frametitle{Building parsed data \ldots}
\begin{lstlisting}
-from pylab import pie
-
science = {}
for record in open('sslc1.txt'):
@@ -317,9 +342,9 @@
if region_code not in science:
science[region_code] = 0
-score_str = fields[4].strip()
+score_str = fields[6].strip()
-score = int(score_str) if
+score = int(score_str) if \
score_str != 'AA' else 0
if score > 90:
@@ -327,17 +352,25 @@
\end{lstlisting}
\end{frame}
+\begin{frame}[fragile]
+ \frametitle{Building parsed data \ldots}
+ \begin{lstlisting}
+print science
+print science.keys()
+print science.values()
+ \end{lstlisting}
+\end{frame}
+
\subsection{Visualizing data}
\begin{frame}[fragile]
- \frametitle{Pie charts}
+ \frametitle{Pie chart}
\small
\begin{lstlisting}
-figure(1)
pie(science.values(),
- labels=science.keys())
+ labels = science.keys())
title('Students scoring 90% and above
in science by region')
-savefig('/tmp/science.png')
+savefig('science.png')
\end{lstlisting}
\begin{columns}
\column{5.25\textwidth}
@@ -345,148 +378,65 @@
\includegraphics[height=2in, interpolate=true]{data/science}
\column{0.8\textwidth}
\end{columns}
- \inctime{5}
+ \inctime{10}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Problem statement}
+ \emphbar{b. Print mean, median and standard deviation of math scores for all regions combined.}
\end{frame}
\begin{frame}[fragile]
- \frametitle{Building data for all subjects \ldots}
+ \frametitle{Building data for statistics}
\begin{lstlisting}
-from pylab import pie
-from scipy import mean, median, std
-from scipy import stats
+math_scores = []
-scores = [[], [], [], [], []]
-ninety_percents = [{}, {}, {}, {}, {}]
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Building data for all subjects \ldots}
- \begin{lstlisting}
for record in open('sslc1.txt'):
record = record.strip()
fields = record.split(';')
- region_code = fields[0].strip()
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Building data for all subjects \ldots}
- \small
- \begin{lstlisting}
-for i, field in enumerate(fields[3:8]):
- if region_code not in ninety_percents[i]:
- ninety_percents[i][region_code] = 0
-
- score_str = field.strip()
- score = int(score_str) if
+ score_str = fields[5].strip()
+ score = int(score_str) if \
score_str != 'AA' else 0
- scores[i].append(score)
-
- if score > 90:
- ninety_percents[i][region_code] += 1
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Consolidating data}
- \begin{lstlisting}
-subj_total = []
-for subject in ninety_percents:
- subj_total.append(sum(
- subject.values()))
+ math_scores.append(score)
\end{lstlisting}
\end{frame}
-\begin{frame}[fragile]
- \frametitle{Pie charts}
- \begin{lstlisting}
-figure(2)
-pie(subj_total, labels=['English',
- 'Hindi', 'Maths', 'Science',
- 'Social'])
-title('Students scoring more than
- 90% by subject(All regions
- combined).')
-savefig('/tmp/all_regions.png')
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Pie charts}
- \includegraphics[height=3in, interpolate=true]{data/all_regions}
-\end{frame}
-
\subsection{Obtaining statistics}
\begin{frame}[fragile]
\frametitle{Obtaining statistics}
- \begin{block}{Statistics: Mean}
+ \begin{block}{Exercise}
Obtain the mean of Math scores
\end{block}
\end{frame}
\begin{frame}[fragile]
- \frametitle{Obtaining statistics: Solution}
- \begin{block}{Statistics: Mean}
- Obtain the mean of Math scores
- \end{block}
- \begin{lstlisting}
-math_scores = scores[2]
-total = 0
-for i, score in enumerate(math_scores):
- total += score
-
-mean = total / (i + 1)
-print "Mean: ", mean
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
- \frametitle{Obtaining statistics: Another solution}
- \begin{block}{Statistics: Mean}
- Obtain the mean of Math scores
- \end{block}
- \begin{lstlisting}
-math_scores = scores[2]
-mean = sum(math_scores) /
- len(math_scores)
- \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{NumPy arrays}
- \begin{itemize}
- \item NumPy provides arrays
- \item arrays are very efficient and powerful
- \item Very easy to perform element-wise operations - \typ{+, -, *, /, \%}
- \begin{lstlisting}
-In [1]: a = array([1, 2, 3])
-In [2]: b = array([4, 5, 6])
-
-In [3]: a + b
-Out[3]: array([5, 7, 9])
- \end{lstlisting}
- \item Very easy to compute statistics
- \end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
\frametitle{Obtaining statistics}
\begin{lstlisting}
-math_scores = array(scores[2])
-
print "Mean: ", mean(math_scores)
print "Median: ", median(math_scores)
-print "Mode: ", stats.mode(math_scores)
-
print "Standard Deviation: ",
std(math_scores)
\end{lstlisting}
- \inctime{15}
+ \inctime{10}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Obtaining statistics: efficiently!}
+ \begin{lstlisting}
+math_array = array(math_scores)
+
+print "Mean: ", mean(math_array)
+
+print "Median: ", median(math_array)
+
+print "Standard Deviation: ",
+ std(math_array)
+ \end{lstlisting}
+ \inctime{5}
\end{frame}
\begin{frame}[fragile]
@@ -494,37 +444,9 @@
\begin{itemize}
\item Dictionaries for storing data
\item Facilities for drawing pie charts
- \item NumPy arrays for efficient array manipulations
- \item Functions for statistical computations - mean, median, mode, standard deviation
+ \item Efficient array manipulations
+ \item Functions for statistical computations - mean, median, standard deviation
\end{itemize}
\end{frame}
-\section{Least square fit}
-\begin{frame}
-\frametitle{L vs $T^2$ \ldots}
-Let's go back to the L vs $T^2$ plot
-\begin{itemize}
-\item We first look at obtaining $T^2$ from T
-\item Then, we look at plotting a Least Squares fit
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Dealing with data whole-sale}
-\begin{lstlisting}
-In []: for t in T:
- ....: TSq.append(t*t)
-\end{lstlisting}
-\begin{itemize}
-\item This is not very efficient
-\item We are squaring element after element
-\item We use arrays to make this efficient
-\end{itemize}
-\begin{lstlisting}
-In []: L = array(L)
-In []: T = array(T)
-In []: TSq = T*T
-\end{lstlisting}
-\end{frame}
-
\end{document}