MATLAB Demysti ed in .NET

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MATLAB Demysti ed
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What this loop does is it creates an array with individual elements repeated by frequency:
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So we have replaced the approach we used in the last section of having two arrays, one with the given age and one with the frequency at that age, by a single array that has each age repeated the given number of times We can use this raw data array with the built-in MATLAB functions to compute statistical information For example, the mean or average age of the employees is:
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>> ave = mean(raw) ave = 307308
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We might also be interested in the median This tells us the age for which half the employees are younger, and half are older:
>> md = median(raw) md = 31
The standard deviation is:
>> sigma = std(raw) sigma = 83836
CHAPTER 4 Statistics/Intro to Programming
If the standard deviation is small, that means most of the data is near the mean value If it is large, then the data is more scattered Since our bin size is 1 year in this case, an 84 year standard deviation indicates the latter situation applies to this data Let s plot a scaled frequency bar chart to look at the shape of the data The rst step is to calculate the area of the data:
area = binwidth*sum(f_abs);
Now we scale it:
scaled_data = f_abs/area;
And generate a plot:
bar(bins,scaled_data),xlabel('Age'),ylabel('Scaled Frequency')
The result is shown in Figure 4-6 As you can see from the plot, the data doesn t t neatly around the mean, which is about 31 years For a contrast let s consider another of ce with a nice distribution Suppose that the employees range in age 17 34 with the following frequency distribution:
f_abs = [2, 1, 0, 0, 5, 4, 6, 7, 8, 6, 4, 3, 2, 2, 1, 0, 0, 1];
016 014 012 Scaled frequency 01 008 006 004 002 0 15
30 Age
Figure 4-6
Age data that has a large standard deviation
MATLAB Demysti ed
035 03 025 Scaled frequency 02 015 01 005 0 16
26 Age
Figure 4-7
A data set with a smaller standard deviation
If we go through the same process with this data, we get the scaled frequency bar chart shown in Figure 4-7 The basic statistical data for this set of employees is:
>> mu = mean(raw) mu = 246538 >> med = median(raw) med = 25 >> sigma = std(raw) sigma = 33307
The standard deviation is much smaller and we can see it in the scaled frequency plot It is approaching the shape of a Gaussian or bell curve, which we show in Figure 4-8
CHAPTER 4 Statistics/Intro to Programming
exp( (x 25)2) 1
0 23 235 24 245 25 x 255 26 265 27
Figure 4-8
A bell curve with a mean of 25 years
When the data ts a Gaussian distribution, the standard deviation can be used to characterize the data to determine the probability of it falling at a certain value Let s just treat the last data set as if this were the case The standard deviation is denoted s while the mean is denoted by m Then the percentage of the graph that lies in the ranges: m - s x < m + s , m - 2s x < m + 2s , and m - 3s x m + 3s is 68%, 96%, and 997%, respectively Using the previous set of age data, the standard deviation and mean were found to be:
sigma = 33307 >> mu mu = 246538
MATLAB Demysti ed
About 68% of the ages will be in 1 standard deviation of the mean, that is, between mu sigma = 213232 years and mu + sigma = 279845 years Going further, 96% of the ages will be between mu 2*sigma = 179925 years and mu + 2* sigma = 313152 years The correspondence is not exact, because our data set is not exactly a bell curve, but we are illustrating the idea and how you could use MATLAB to analyze data that is close to a bell curve
More MATLAB Programming Tips
Earlier we wrote a script le (m) to implement a function which could be written up like computer code Let s digress a bit and round out the chapter looking at a few more programming structures First let s see how to get data from the user or from yourself in real time at a computer prompt This is done using the input function To use input, you set a variable you want to use to store the input data equal to the command, which takes a quote-delimited string as argument When the statement is executed MATLAB prints your string to the command window and waits for data to be typed in When the return key is hit, it assigns whatever data the user typed to the appropriate variable Let s concoct a simple example to see how this works Suppose that we want to get the number of square feet of a house, and given that the price of homes in Podunk, Maine is $10 per square foot, we output the total asking price of the house We can ask for and get the data using the following commands First, since we are working with nancial data here, we tell MATLAB to display results with the bank format Then we set our rate per square foot
>> format bank >> rate = 10;
Now let s ask the user to enter the square footage of the house by politely asking for it with the input command:
>> sqft = input('Enter total sqft of house: ')
MATLAB responds thus:
Enter total sqft of house:
If you enter these statements, MATLAB will be waiting patiently with a blinking cursor just to the right of this statement Let s say we enter 1740 The result is:
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