--- a/statistics.txt	Tue Mar 30 14:45:12 2010 +0530
+++ b/statistics.txt	Tue Mar 30 19:17:12 2010 +0530
@@ -2,10 +2,15 @@
 
 In the previous tutorial we saw the `for' loop and lists. Here we shall look into
 calculating mean for the same pendulum experiment and then move on to calculate
-the mean, median and mode for a very large data set.
+the mean, median and standard deviation for a very large data set.
+
+Let's start with calculating the mean acceleration due to gravity based on the data from pendulum.txt.
 
+We first create an empty list `g_list' to which we shall append the values of `g'.
+In []: g_list = []
 
-In []: g_list = []
+For each pair of `L' and `t' values in the file `pendulum.txt' we calculate the 
+value of `g' and append it to the list `g_list'
 In []: for line in open('pendulum.txt'):
   ....     point = line.split()
   ....     L = float(point[0])
@@ -13,40 +18,60 @@
   ....     g = 4 * pi * pi * L / (t * t)
   ....     g_list.append(g)
 
+We proceed to calculate the mean of the value of `g' from the list `g_list'. 
+Here we shall show three ways of calculating the mean. 
+Firstly, we calculate the sum `total' of the values in `g_list'.
 In []: total = 0
 In []: for g in g_list:
  ....:     total += g
  ....:
 
+Once we have the total we calculate by dividing the `total' by the length of `g_list'
+
 In []: g_mean = total / len(g_list)
 In []: print 'Mean: ', g_mean
 
+The second method is slightly simpler. Python provides a built-in function called "sum()" that computes the sum of all the elements in a list. 
 In []: g_mean = sum(g_list) / len(g_list)
 In []: print 'Mean: ', g_mean
 
+The third method is the simplest. Python provides a built-in function `mean' that
+calculates the mean of all the elements in a list.
 In []: g_mean = mean(g_list)
 In []: print 'Mean: ', g_mean
 
+Python provides support for dictionaries. Dictionaries are key value pairs. Lists are indexed by integers while dictionaries are indexed by strings. For example:
+In []: d = {'png' : 'image',
+      'txt' : 'text', 
+      'py' : 'python'} 
+is a dictionary. The first element in the pair is called the `key' and the second 
+is called the `value'. The key always has to be a string while the value can be 
+of any type.
 
-In []: d = {'png' : 'image file',
-      'txt' : 'text file', 
-      'py' : 'python code'
-      'java': 'bad code', 
-      'cpp': 'complex code'}
+Dictionaries are indexed using their keys as shown
+In []: d['txt']
+Out[]: 'text'
 
-In []: d['txt']
-Out[]: 'text file'
+In []: d['png']
+Out[]: 'image'
 
+The dictionaries can be searched for the presence of a certain key by typing
 In []: 'py' in d
 Out[]: True
 
 In []: 'jpg' in d
 Out[]: False
+Please note the values cannot be searched in a dictionaries.
 
 In []: d.keys()
-Out[]: ['cpp', 'py', 'txt', 'java', 'png']
+Out[]: ['py', 'txt', 'png']
+is used to obtain the list of all keys in a dictionary
 
 In []: d.values()
-Out[]: ['complex code', 'python code',
-        'text file', 'bad code', 
-        'image file']
+Out[]: ['python', 'text', 'image']
+is used to obtain the list of all values in a dictionary
+
+In []: d
+Out[]: {'png': 'image', 'py': 'python', 'txt': 'text'}
+Please observe that dictionaries do not preserve the order in which the items
+were entered. The order of the elements in a dictionary should not be relied upon.