Mean, Variance, Squaring

This is a discussion on Mean, Variance, Squaring within the C++ Programming forums, part of the General Programming Boards category; Hello, Does C++ have built in function for finding mean and variance of a sequence of numbers? Also if I ...

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    Mean, Variance, Squaring

    Hello,

    Does C++ have built in function for finding mean and variance of a sequence of numbers?

    Also if I have an expression

    (a - b) and I would like it squared, is there an equivalent to Matlab's
    (a - b)^2?

    The reason I ask that is that if I have to write out variance calculation mannually, I'd have to say:
    Code:
    sqrt( (a-mean)^2 + (b-mean)^2 + ... + (n-mean)^2)/n)
    
    // My inputs have quite long names and it would look clumbersome to say
    
    sqrt( (a-mean)*(a-mean) + (b-mean)* (b-mean) + ... + (n-mean)*(n-mean))/n)
    Any suggestions please?

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    Just a pushpin. bernt's Avatar
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    (a - b) and I would like it squared, is there an equivalent to Matlab's
    (a - b)^2?
    The C math library (link) has some stuff like that. Nothing terribly special though - just all the basic functions (e^x, log, pow, trig, etc). So to answer your question:
    Code:
    #include <math.h> //#include <cmath> instead for C++ environments
    ...
    
    double ans = pow(a, b); //double = a^b
    but IMO it's just easier to write out the multiplication for squares.

    sqrt( (a-mean)*(a-mean) + (b-mean)* (b-mean) + ... + (n-mean)*(n-mean))/n)
    You could instead add the numbers in a loop. So instead of using variables a-n, you have an array of numbers.
    Code:
    double numbers[n];
    //fill array with values here: numbers[0]=3, numbers[1] =6, etc.
    
    double sum=0;
    int i;
    for (i=0; i<n; i++) {
        sum+=(numbers[i]-mean)*(numbers[i]-mean);
    }
    
    double answer = sqrt(sum / n);
    Consider this post signed

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    Thank you very much, yes I've used the last idea you suggested. It is looking much neater that way.

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    Registered User hk_mp5kpdw's Avatar
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    If/when you get more familiar with the STL, you can look at the numeric header which has some neat items in it. The inner_product function in particular looks like it can be used to compute variance in a somewhat compact form:
    Code:
    #include <iostream>
    #include <numeric>
    #include <functional>
    #include <cmath>
    
    struct deviation_func
    {
        double mean;
        deviation_func(double _mean) : mean(_mean) {}
        double operator()(double lhs,double rhs)
        {
            return (lhs-mean) * (rhs-mean);
        }
    };
    
    int main()
    {
        double arr[] = {2,4,4,4,5,5,7,9};
        const int num_vals = sizeof(arr)/sizeof(arr[0]);
        double mean = std::accumulate(arr,arr+num_vals,0.0)/num_vals;
        deviation_func foo(mean);
        double variance = std::inner_product(arr,arr+num_vals,arr,0.0,std::plus<double>(),foo)/num_vals;
        double standard_dev = std::sqrt(variance);
    
        std::cout << "Arithmetic mean is    : " << mean << std::endl;
        std::cout << "Population variance is: " << variance << std::endl;
        std::cout << "Standard deviation is : " << standard_dev << std::endl;
    
        return 0;
    }
    Whether it actually makes things more complicated looking or not is a matter of individual opinion. A simple loop might be best in many cases for clarity. Output of above program is below:
    Attached Images Attached Images  
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    -Christopher Hitchens

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