Dada una array, necesitamos calcular la varianza y la desviación estándar de los elementos de la array.
Ejemplos:
Input : arr[] = [1, 2, 3, 4, 5]
Output : Variance = 2
Standard Deviation = 1
Input : arr[] = [7, 7, 8, 8, 3]
Output : Variance = 3
Standard Deviation = 1
Hemos discutido el programa para encontrar la media de una array .
La media es el promedio del elemento.
Media de arr[0..n-1] = ∑(arr[i]) / n
donde 0 <= i < n
La varianza es la suma de las diferencias al cuadrado de la media dividida por el número de elementos.
Varianza = ∑(arr[i] – media) 2 / n
La desviación estándar es la raíz cuadrada de la varianza
Desviación estándar = √(varianza)
Consulte Media, varianza y desviación estándar para obtener más detalles.
A continuación se muestra la implementación del enfoque anterior:
C++
// CPP program to find variance
// and standard deviation of
// given array.
#include <bits/stdc++.h>
using namespace std;
// Function for calculating variance
int variance(int a[], int n)
{
// Compute mean (average of elements)
int sum = 0;
for (int i = 0; i < n; i++)
sum += a[i];
double mean = (double)sum /
(double)n;
// Compute sum squared
// differences with mean.
double sqDiff = 0;
for (int i = 0; i < n; i++)
sqDiff += (a[i] - mean) *
(a[i] - mean);
return sqDiff / n;
}
double standardDeviation(int arr[],
int n)
{
return sqrt(variance(arr, n));
}
// Driver Code
int main()
{
int arr[] = {600, 470, 170, 430, 300};
int n = sizeof(arr) / sizeof(arr[0]);
cout << "Variance: "
<< variance(arr, n) << "\n";
cout << "Standard Deviation: "
<< standardDeviation(arr, n) << "\n";
return 0;
}
Java
// Java program to find variance
// and standard deviation of
// given array.
import java.io.*;
class GFG
{
// Function for calculating
// variance
static double variance(double a[],
int n)
{
// Compute mean (average
// of elements)
double sum = 0;
for (int i = 0; i < n; i++)
sum += a[i];
double mean = (double)sum /
(double)n;
// Compute sum squared
// differences with mean.
double sqDiff = 0;
for (int i = 0; i < n; i++)
sqDiff += (a[i] - mean) *
(a[i] - mean);
return (double)sqDiff / n;
}
static double standardDeviation(double arr[],
int n)
{
return Math.sqrt(variance(arr, n));
}
// Driver Code
public static void main (String[] args)
{
double arr[] = {600, 470, 170, 430, 300};
int n = arr.length;
System.out.println( "Variance: " +
variance(arr, n));
System.out.println ("Standard Deviation: " +
standardDeviation(arr, n));
}
}
// This code is contributed by vt_m.
Python 3
# Python 3 program to find variance
# and standard deviation of
# given array.
import math
# Function for calculating variance
def variance(a, n):
# Compute mean (average of
# elements)
sum = 0
for i in range(0 ,n):
sum += a[i]
mean = sum /n
# Compute sum squared
# differences with mean.
sqDiff = 0
for i in range(0 ,n):
sqDiff += ((a[i] - mean)
* (a[i] - mean))
return sqDiff / n
def standardDeviation(arr, n):
return math.sqrt(variance(arr, n))
# Driver Code
arr = [600, 470, 170, 430, 300]
n = len(arr)
print("Variance: ", int(variance(arr, n)))
print("Standard Deviation: ",
round(standardDeviation(arr, n), 3))
# This code is contributed by Smitha
C#
// C# program to find variance and
// standard deviation of given array.
using System;
class GFG
{
// Function for calculating
// variance
static float variance(double []a,
int n)
{
// Compute mean (average
// of elements)
double sum = 0;
for (int i = 0; i < n; i++)
sum += a[i];
double mean = (double)sum /
(double)n;
// Compute sum squared
// differences with mean.
double sqDiff = 0;
for (int i = 0; i < n; i++)
sqDiff += (a[i] - mean) *
(a[i] - mean);
return (float)sqDiff / n;
}
static float standardDeviation(double []arr,
int n)
{
return (float)Math.Sqrt(variance(arr, n));
}
// Driver Code
public static void Main ()
{
double []arr = {600, 470, 170, 430, 300};
int n = arr.Length;
Console.WriteLine( "Variance: " +
variance(arr, n));
Console.WriteLine ("Standard Deviation: " +
standardDeviation(arr, n));
}
}
// This code is contributed by vt_m.
PHP
<?php
// PHP program to find variance
// and standard deviation of
// given array.
// Function for calculating.
// variance
function variance( $a, $n)
{
// Compute mean (average
// of elements)
$sum = 0;
for ( $i = 0; $i < $n; $i++)
$sum += $a[$i];
$mean = $sum / $n;
// Compute sum squared
// differences with mean.
$sqDiff = 0;
for ( $i = 0; $i < $n; $i++)
$sqDiff += ($a[$i] - $mean) *
($a[$i] - $mean);
return $sqDiff / $n;
}
function standardDeviation($arr, $n)
{
return sqrt(variance($arr, $n));
}
// Driver Code
$arr = array(600, 470, 170, 430, 300);
$n = count($arr);
echo "Variance: " ,
variance($arr, $n) , "\n";
echo"Standard Deviation: " ,
standardDeviation($arr, $n) ,"\n";
// This code is contributed by anuj_67.
?>
Javascript
<script>
// JavaScript program to find variance and
// standard deviation of given array.
// Function for calculating
// variance
function variance(a, n)
{
// Compute mean (average of elements)
var sum = 0;
for (var i = 0; i < n; i++){
sum += a[i];
}
var mean = sum / n;
// Compute sum squared
// differences with mean.
var sqDiff = 0;
for (var i = 0; i < n; i++) {
sqDiff += (a[i] - mean) * (a[i] - mean);
}
return sqDiff / n;
}
function standardDeviation(arr , n)
{
return Math.sqrt(variance(arr, n));
}
// Driver Code
var arr = [600, 470, 170, 430, 300]
var n = arr.length;
document.write( "Variance: " +
variance(arr, n) + "<br>");
document.write ("Standard Deviation: " +
standardDeviation(arr, n).toFixed(3));
</script>
Producción
Variance: 21704 Standard Deviation: 147.323
La complejidad temporal del programa es O(n) .
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Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA