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:

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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)

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Any suggestions please?

Quote:

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

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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:

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#include <math.h> //#include <cmath> instead for C++ environments
...

double ans = pow(a, b); //double = a^b

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but IMO it's just easier to write out the multiplication for squares.

Quote:

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sqrt( (a-mean)*(a-mean) + (b-mean)* (b-mean) + ... + (n-mean)*(n-mean))/n)

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You could instead add the numbers in a loop. So instead of using variables a-n, you have an array of numbers.

Code:

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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);

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

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:

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#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;
}

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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: