Deviation and Variance

Question

This assignment requires obtaining the deviation and variance of \$n\$ numbers stored in one single array. Is there any way to make this code more efficient?

#include <iostream>
#include <cmath>

using namespace std;
int main()

{
    const int arrSize = 14;
    double average , sum = 0 , dev = 0;
    double deviation[arrSize];

    int grades[arrSize] = { 89, 95, 72, 83, 99, 54, 86, 75, 92, 73, 79, 75, 82, 73 };

    // Calculating the average
    for ( int i = 0; i < arrSize; i++ )
    {
        sum += grades[i];
        average = ( sum / arrSize );
    }
    cout << "average is : " << average << endl;
    cout << endl;

    //Calculating the deviation and variance

    double sumVar = 0 , totalVar = 0;
    for ( int i = 0; i < arrSize; i++ )
    {
        deviation[i] = ( grades[i] - average );

        cout << "Grades = " << grades[i] << " and deviation is = " << deviation[i] << endl;

        double variance = pow( deviation[i] , 2 );
        sumVar = sumVar + variance;
        totalVar = ( sumVar / arrSize );


    }
    cout << endl;
    cout << "variance = " << totalVar << endl;

    system( "pause" );
    return 0;
}

Answer 1

efficiency

Yes, this can be improved.

One obvious problem is that you're re-computing your average and your standard deviation on every iteration of a loop, even though only the last result (after the last iteration) is ever actually used.

For example:

for (int i = 0; i < arrSize; i++)
{
    sum += grades[i];
    average = (sum / arrSize);
}

You're computing average on every iteration, but only need or use the last value you compute. You can compute it once with code like:

for (int i = 0; i < arrSize; i++)
{
    sum += grades[i];
}
average = (sum / arrSize);

Your computation of the standard deviation is much the same way.

Use of pow

I'd avoid using pow to compute a square. It often imposes quite a bit of overhead, so pow(deviation[i], 2) will often be substantially slower than deviation[i]*deviation[i].

Formatting

Looking at the code more generally, you really need to fix your indentation.

std::endl

I would advise against using std::end. Normally, you just want '\n', which also gives you a new line, but will nearly always be (much) faster. In the case above, it won't make much difference, but if you're writing a lot of data to a file (for example) the difference can get very large, very quickly (e.g., a slowdown of 8:1 or 10:1 is fairly typical).

Answer 2

So although this is already marked as accepted i would like to add, that if this is indeed C++ you should definitely use containers (std::vector in this case).

That will also allow you to utilize range based loops, which condense everything a little bit. Also you can use the algorithm library too

std::vector<int> grades = { 89, 95, 72, 83, 99, 54, 86, 75, 92, 73, 79, 75, 82, 73 };

// Calculating the average 
// If you ommit the static_cast, the result will be rounded down to the next integer 
double average = (static_cast<double>(std::accumulate(grades.begin(), grades.end(), 0))/ grades.size());

Answer 3

using namespace std;

It is generally considered a poor idea to import all names from a namespace (with some exceptions, such as the namespaces for literals, or if you are actually implementing that namespace). It creates a risk of identifier clashes that could bite you when you compile against future C++ standards.

---

double dev = 0;

Unused variable.

---

system( "pause" );

sh: 1: pause: not found

And you didn't include <cstdlib> for this, anyway.

---

Arithmetic: there's a subtle problem in accumulating int values into a double, which you won't see on such small input sets. As the double re-scales itself, less and less of each int is significant to the sum. For large input sets, you may need to accumulate into a long (or unsigned long if your inputs can't be negative) and only add that to sum when it's about to overflow:

long acc = 0;
for ( int i = 0; i < arrSize; i++ )
{
    if (grades[i] > LONG_MAX-acc) {
        sum += acc;
        acc = 0;
    }
    acc += grades[i];
}
sum += acc;

(You'll need to include climits to define LONG_MAX)

---

General: it's a good idea to separate your printing from your algorithm. Create a function to do the computation; then your main() should call it appropriately and print the output. To get you started:

std::pair<double, double> mean_and_variance<const std::vector<int>& values);