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CHAPTER 4 Statistics/Intro to Programming
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s = x*N; ave = sum(s)/total; end
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Once the function is written, we need to save it so that it can be used in the command window MATLAB will save your m les in the work folder Let s return to the command window and see how we can use the function At an area law of ce, there are employees with the following ages:
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Age 20 25 38 43 55 Number of Employees 2 3 4 2 3
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Let s create the age array, which corresponds to x in our function:
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>> age = [20, 25, 38, 43, 55];
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Next we create an array called num which corresponds to N in our function:
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>> num = [2, 3, 4, 2, 3];
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Calling the function, we nd the average age is:
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ans = 37
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Before moving on let s test our function to make sure it reports the error message when we pass two arrays that aren t the same size Let s try:
>> a = [1,2,3]; >> b = [1,2,3,4,5,6];
When we call myaverage we get the error message:
>> myaverage(a,b)
Error: Arrays must be same dimensions
MATLAB Demysti ed
Programming with For Loops
A For Loop is an instruction to MATLAB telling it to execute the enclosed statements a certain number of times The syntax used in a For Loop is:
for index = start: increment : nish statements end
We can illustrate this idea by writing a simple function that sums the elements in a row or column vector If we leave the increment parameter out of the For Loop statement, MATLAB assumes that we want the increment to be one The rst step in our function is to declare the function name and get the size of the array passed to our function:
function sumx = mysum(x) %get number of elements num = size(x);
We ve added a new programming element here we included a comment A comment is an explanatory line for the reader that is ignored by MATLAB We indicate comments by placing a % character in the rst column of the line Now let s create a variable to hold the sum and initialize it to zero:
%initialize total sumx = 0;
Now we use a For Loop to step through the elements in the column vector 1 at a time:
for i = 1:num(2) sumx = sumx + x(i); end
When writing functions, be sure to add a semicolon at the end of each statement unless you want the result to be displayed on screen
Calculating Standard Deviation and Median
Let s return to using the basic statistical analysis tools in MATLAB to nd the standard deviation and median of a set of discrete data We assume the data is given in terms of a frequency or number of data points Once again, as a simple example
CHAPTER 4 Statistics/Intro to Programming
we consider a set of employees at an of ce, and we are given the number of employees at each age Suppose that there are: Two employees aged 17 One employee aged 18 Three employees aged 21 One employee aged 24 One employee aged 26 Four employees aged 28 Two employees aged 31 One employee aged 33 Two employees aged 34 Three employees aged 37 One employee aged 39 Two employees aged 40 Three employees aged 43 The rst thing we will do is create an array of absolute frequency data This is the array N( j) that we had been using in the previous sections This time we will have an entry for each age, so we put a 0 if no employees are listed with the given age Let s call it f_abs for absolute frequency:
f_abs = [2, 1, 0, 0, 3, 0, 0, 1, 0, 1, 0, 4, 0, 0, 2, 0, 1, 2, 0, 0, 3, 0, 1, 2, 0, 0, 3];
We are binning the data, so let s de ne a bin width Since we are measuring this in one year increments, we set our bin width to one:
binwidth = 1;
Now we create an array that represents the ages ranged from 17 to 43 with a binwidth of one year:
bins = [17:bin width:43];
Now we collect the raw data We use a For Loop to sweep through the data as follows:
raw = []; for i = 1:length(f_abs) if f_abs(i) > 0 new = bins(i)*ones(1,f_abs(i));
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