实施均值标准误的程序

均值标准误差(SEM)用于根据总体均值估算样本均值离散度。标准误差与样本平均值一起用于估计平均值的近似置信区间。也称为平均值或测量的标准误差，通常用SE，SEM或S _E表示。

例子：

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

样本平均值

样本标准偏差

估计均值的标准误

解释：

given an array arr[] = {78.53, 79.62, 80.25, 81.05, 83.21, 83.46}
and the task is to find standard error of mean.
mean = (78.53 + 79.62 + 80.25 + 81.05 + 83.21 + 83.46) / 6
= 486.12 / 6
= 81.02
Sample Standard deviation = sqrt((78.53 – 81.02)² + (79.62- 81.02)² + . . .
+ (83.46 – 81.02)² / (6 – 1))
= sqrt(19.5036 / 5)
= 1.97502
Standard error of mean = 1.97502 / sqrt(6)
= 0.8063

C++

// C++ Program to implement 
// standard error of mean.
#include 
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.

输出：

0.8063