### Computing Sum, Mean, Variance, Standard Deviation, Coefficient of Variation, Smallest, Biggest, Median, Range, and Mode using C++

This is a programming tutorial for computing sum, mean, variance, standard deviation, coefficient of variation, smallest number, biggest number, median, range, and mode of *n* numbers using C++. In this tutorial, I have used Dev C++ v5.11 software for compiling the C++ program.

The formula for calculating sum, mean, variance, standard deviation, coefficient of variation, smallest number, biggest number, median, range, and mode of set of *n* numbers is given below:

Description | Formula |
---|---|

Number of Samples | n |

Sum (Total) | \[\sum\limits_{i=1}^{n}{{{x}_{i}}}={{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}\] |

Mean (Average) | \[\bar{x}=\frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}}{n}\] |

Variance | \[{{\operatorname{var}}_{x}}=\frac{\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}{n-1}\] |

Standard Deviation | \[{{\sigma }_{x}}=\sqrt{\frac{\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}}{n-1}}\] |

Coefficient of Variance | \[c{{v}_{x}}=\frac{{{\sigma }_{x}}}{{\bar{x}}}\times 100%\] |

Minimum (Smallest Number) | x_{1} |

Maximum (Biggest Number) | x_{n} |

Median (Middle) | \[m{{d}_{x}}={{x}_{\left( \frac{n-1}{2} \right)}},\ if\ n\ is\ odd\] |

\[m{{d}_{x}}=\frac{{{x}_{\left( \frac{n}{2} \right)}}+{{x}_{\left( \frac{n}{2}+1 \right)}}}{2},\ if\ n\ is\ even\] | |

Mode (Most Common) | frequency_{max} |

#### Source Code

```
// Sum, Mean, Variance, Standard Deviation, Coefficient of Variation, Smallest, Biggest, Median, Range, and Mode.
#include <iostream>
#include <sstream>
#include <string>
#include <conio.h>
#include <math.h>
#include <iomanip>
using namespace std;
string n2s(double y)
{
std::stringstream p;
std::string q;
p << y;
p >> q;
return q;
}
int main()
{
int i, j, n, x, max, mn;
double t, a[20], b[20], s[20], s1, z, m, cv, dev, var, sum, mean, median, range, sd;
string mode;
sum = x = dev = max = mn = range = 0;
mode = "";
cout << "\nSum, Mean, Variance, Standard Deviation, Coefficient of Variation, Smallest, Biggest, Median, Range, and Mode\n\n";
cout << "\nHow many numbers? ";
cin >> n;
cout << "\nEnter the numbers: ";
for (i = 0; i < n; i++) {
cin >> a[i];
s[i] = a[i];
sum += a[i];
}
mean = sum / n;
system("cls");
cout << "\nInput Numbers: ";
for (i = 0; i < n; i++) {
i < n-1 ? cout << a[i] << ", " : cout << "and " << a[i] << endl;
dev += pow((a[i] - mean), 2);
}
var = dev / (n - 1);
sd = sqrt(var);
cv = (sd / mean) * 100;
for (i = 0; i < n; i++) {
for (j = i + 1; j < n; j++) {
if (s[i] > s[j]) {
t = s[i];
s[i] = s[j];
s[j] = t;
}
}
}
s1 = s[0];
cout << "\nSorted Numbers: ";
for(i = 0; i < n; i++) {
i < n-1 ? cout << s[i] << ", " : cout << "and " << s[i] << endl;
b[i+1] = s[i];
}
range = s[n-1] - s[0];
cout << "\n" << setw(29) << "Total Numbers : " << n << endl;
cout << "\n" << setw(29) << "Sum (Total) : " << sum << endl;
cout << "\n" << setw(29) << "Mean (Average) : " << mean << endl;
cout << "\n" << setw(29) << "Variance (\xE5\xFD) : " << var << endl;
cout << "\n" << setw(29) << "Standard Deviation : " << sd << endl;
cout << "\n" << setw(29) << "Coefficient of Variation : " << cv << " \%" << endl;
if (n%2 == 0) {
median = (b[n/2] + b[(n/2)+1]) / 2;
} else {
median = b[(n+1)/2];
}
cout << "\n" << setw(29) << "Smallest Number : " << s[0] << endl;
cout << "\n" << setw(29) << "Biggest Number : " << s[n-1] << endl;
cout << "\n" << setw(29) << "Median (Middle) : " << median << endl;
cout << "\n" << setw(29) << "Range (Biggest - Smallest) : " << range << endl;
cout << "\n" << setw(29) << "Mode (Most Common) : ";
for (i = 0; i <= n; i++) {
z = s[i];
if (z == s1) {
x += 1;
if (x > max) {
m = s1;
max = x;
mn++;
mode = n2s(m);
}
} else {
if (x == max && m != s1) {
mode += ", " + n2s(s1);
mn++;
}
s1 = z;
x = 1;
}
}
if (n == mn) {
cout << "No Mode Found" << endl;
} else {
cout << mode << endl;
}
getch();
}
```

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