statistics-script
author amit@thunder
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Adding arrays.txt file , script for arrays tutorial , session 4
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Hello friends and welcome to the third tutorial in the series of tutorials on "Python for scientific computing."
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In the previous tutorial we learnt how to read data from a file and plot the data
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We used 'for' loops and lists to get data in desired format.
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IPython -Pylab also provides with a function 'loadtxt' which can get us data without much hustle.
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We know that, pendulum.txt contains two columns, with length being first and time period is second column, so to get both columns in two separate variables we type
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l, t = loadtxt('pendulum.txt', unpack=True)
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(unpack = True)? will give us all of first column(length) in l and second column(time) in t
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to get more help type 
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loadtxt?
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This is really powerful tool to load data directly from files which are well structured and formatted. It supports many features like getting particular columns. 
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now to get squared values of t we can simply do
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tsq = t*t
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and we dont have to use for loop anymore. This is benefit of arrays. If we try to something similar to lists we cant escape a 'for' loop.
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Now to plot l vs tsq is same as we did in previous session
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plot(l, tsq, 'o')
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Additionally the basic equation for finding Time period of simple pendulum we use equation:
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T = 2*pi*sqrt(L/g)
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In our case we have t and l already, so to find g value for each element we can simply use:
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g = 4*pi^2*L/T^2
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g is array with 90 elements, so we take average of all these values to get acceleration due to gravity('g') by
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print mean(g)
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Mean again is provided by pylab module which calculates average of given set of values.
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There are other handy statistical functions available, such as median, mode, std(for standard deviation) etc.
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So in this small session we have covered 'better' way of loading data from text files.
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Why arrays are better choice then lists in some cases, and how they are helpful during some mathematical operations.
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Thank you!
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In this tutorial we shall learn how to compute statistics using python.
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We also shall learn how to represent data in the form of pie charts.
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Let us start with the most basic need in statistics, the mean.
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We shall calculate the mean acceleration due to gravity using the same 'pendulum.txt' that we used in the previous session.
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As we know, 'pendulum.txt' contains two values in each line. The first being length of pendulum and second the time period.
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To calculate acceleration due to gravity from these values, we shall use the expression T = 2*pi*sqrt(L/g)
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So re-arranging this equation, we get g = 4*pi**2*L/T**2 .
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We shall calculate the value of g for each pair of L and t and then calculate mean of all those g values.
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## if we do loadtxt and numpy arrays then this part will change
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	First we need something to store each value of g that we are going to compute.
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	So we start with initialising an empty list called `g_list'.
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	Now we read each line from the file 'pendulum.txt' and calculate g value for that pair of L and t and then append the computed g to our `g_list'.
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	In []: for line in open('pendulum.txt'):
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	  ....     point = line.split()
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	  ....     L = float(point[0])
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	  ....     t = float(point[1])
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	  ....     g = 4 * pi * pi * L / (t * t)
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	  ....     g_list.append(g)
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	The first four lines of this code must be trivial. We read the file and store the values. 
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	The fifth line where we do g equals to 4 star pi star and so on is the line which calculates g for each pair of L and t values from teh file. The last line simply stores the computed g value. In technical terms appends the computed value to g_list.
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	Let us type this code in and see what g_list contains.
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###############################
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Each value in g_list is the g value computed from a pair of L and t values.
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Now we have all the values for g. We must find the mean of these values. That is the sum of all these values divided by the total no.of values.
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The no.of values can be found using len(g_list)
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So we are left with the problem of finding the sum.
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We shall create a variable and loop over the list and add each g value to that variable.
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lets call it total.
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In []: total = 0 
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In []: for g in g_list:
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 ....:     total += g
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 ....:
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So at of this piece of code we will have the sum of all the g values in the variable total.
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Now calculating mean of g is as simple as doing total divided by len(g_list)
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In []: g_mean = total / len(g_list)
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In []: print 'Mean: ', g_mean
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If we observe, we have to write a loop to do very simple thing such as finding sum of a list of values.
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Python has a built-in function called sum to ease things.
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sum takes a list of values and returns the sum of those values.
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now calculating mean is much simpler.
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we don't have to write any for loop.
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we can directly use mean = sum(g_list) / len(g_list)
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Still calculating mean needs writing an expression.
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What if we had a built-in for calculating mean directly.
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We do have and it is available through the pylab library.
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Now the job of calculating mean is just a function away.
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Call mean(g_list) directly and it gives you the mean of values in g_list.
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Isn't that sweet. Ya and that is why I use python.
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