El error estándar de la media (SEM) se utiliza para estimar la dispersión de la media de la muestra a partir de la media de la población. El error estándar junto con la media de la muestra se usa para estimar los intervalos de confianza aproximados para la media. También se conoce como error estándar de la media o medida, a menudo denotado por SE, SEM o S E.
Ejemplos:
Input : arr[] = {78.53, 79.62, 80.25, 81.05, 83.21, 83.46}
Output : 0.8063
Input : arr[] = {5, 5.5, 4.9, 4.85, 5.25, 5.05, 6.0}
Output : 0.1546
Muestra promedio
Desviación estándar de la muestra
Estimar el error estándar de la media
Explicación:
dada una array arr[] = {78.53, 79.62, 80.25, 81.05, 83.21, 83.46}
y la tarea es encontrar el error estándar de la media.
media = (78.53 + 79.62 + 80.25 + 81.05 + 83.21 + 83.46) / 6
= 486.12 / 6
= 81.02
Muestra Desviación estándar = sqrt((78.53 – 81.02) 2 + (79.62- 81.02) 2 + . . .
+ (83.46 – 81.02) 2 / (6 – 1))
= sqrt(19.5036 / 5)
= 1.97502
Error estándar de la media = 1.97502 / sqrt(6)
= 0.8063
C++
// C++ Program to implement
// standard error of mean.
#include <bits/stdc++.h>
using namespace std;
// Function to find sample mean.
float mean(float arr[], int n)
{
// loop to calculate
// sum of array elements.
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to calculate sample
// standard deviation.
float SSD(float arr[], int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + (arr[i] - mean(arr, n))
* (arr[i] - mean(arr, n));
return sqrt(sum / (n - 1));
}
// Function to calculate sample error.
float sampleError(float arr[], int n)
{
// Formula to find sample error.
return SSD(arr, n) / sqrt(n);
}
// Driver function
int main()
{
float arr[] = { 78.53, 79.62, 80.25,
81.05, 83.21, 83.46 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << sampleError(arr, n);
return 0;
}
Java
// Java Program to implement
// standard error of mean.
class GFG {
// Function to find sample mean.
static float mean(float arr[], int n)
{
// loop to calculate
// sum of array elements.
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to calculate sample
// standard deviation.
static float SSD(float arr[], int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + (arr[i] - mean(arr, n))
* (arr[i] - mean(arr, n));
return (float)Math.sqrt(sum / (n - 1));
}
// Function to calculate sample error.
static float sampleError(float arr[], int n)
{
// Formula to find sample error.
return SSD(arr, n) / (float)Math.sqrt(n);
}
// Driver function
public static void main(String[] args)
{
float arr[] = { 78.53f, 79.62f, 80.25f,
81.05f, 83.21f, 83.46f };
int n = arr.length;
System.out.println(sampleError(arr, n));
}
}
// This code is contributed
// by prerna saini
Python3
# Python 3 Program to implement # standard error of mean. import math # Function to find sample mean. def mean(arr, n) : # loop to calculate # sum of array elements. sm = 0 for i in range(0,n) : sm = sm + arr[i] return sm / n # Function to calculate sample # standard deviation. def SSD(arr, n) : sm = 0 for i in range(0,n) : sm = sm + (arr[i] - mean(arr, n)) * (arr[i] - mean(arr, n)) return (math.sqrt(sm / (n - 1))) # Function to calculate sample error. def sampleError(arr, n) : # Formula to find sample error. return SSD(arr, n) / (math.sqrt(n)) # Driver function arr = [ 78.53, 79.62, 80.25, 81.05, 83.21, 83.46] n = len(arr) print(sampleError(arr, n)) # This code is contributed # by Nikita Tiwari.
C#
// C# Program to implement
// standard error of mean.
using System;
class GFG {
// Function to find sample mean.
static float mean(float []arr, int n)
{
// loop to calculate
// sum of array elements.
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + arr[i];
return sum / n;
}
// Function to calculate sample
// standard deviation.
static float SSD(float []arr, int n)
{
float sum = 0;
for (int i = 0; i < n; i++)
sum = sum + (arr[i] - mean(arr, n))
* (arr[i] - mean(arr, n));
return (float)Math.Sqrt(sum / (n - 1));
}
// Function to calculate sample error.
static float sampleError(float []arr, int n)
{
// Formula to find sample error.
return SSD(arr, n) / (float)Math.Sqrt(n);
}
// Driver code
public static void Main()
{
float []arr = {78.53f, 79.62f, 80.25f,
81.05f, 83.21f, 83.46f};
int n = arr.Length;
Console.Write(sampleError(arr, n));
}
}
// This code is contributed by Nitin Mittal.
PHP
<?php
// PHP Program to implement
// standard error of mean.
// Function to find sample mean.
function mean($arr,$n)
{
// loop to calculate
// sum of array elements.
$sum = 0;
for ($i = 0; $i < $n; $i++)
$sum = $sum + $arr[$i];
return $sum / $n;
}
// Function to calculate sample
// standard deviation.
function SSD($arr, $n)
{
$sum = 0;
for ($i = 0; $i < $n; $i++)
$sum = $sum + ($arr[$i] -
mean($arr, $n)) *
($arr[$i] -
mean($arr, $n));
return sqrt($sum / ($n - 1));
}
// Function to calculate
// sample error.
function sampleError($arr, $n)
{
// Formula to find sample error.
return SSD($arr, $n) / sqrt($n);
}
// Driver Code
{
$arr = array(78.53, 79.62, 80.25,
81.05, 83.21, 83.46 );
$n = sizeof($arr) / sizeof($arr[0]);
echo sampleError($arr, $n);
return 0;
}
// This code is contributed by nitin mittal.
?>
Producción:
0.8063
Publicación traducida automáticamente
Artículo escrito por Dharmendra_Kumar y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA