# Program to implement standard error of mean

• Last Updated : 12 Sep, 2022

Standard error of mean (SEM) is used to estimate the sample mean dispersion from the population mean. The standard error along with sample mean is used to estimate the approximate confidence intervals for the mean. It is also known as standard error of mean or measurement often denoted by SE, SEM or SE.

Examples:

```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```

Sample mean

Sample Standard Deviation

Estimate standard error of mean

Explanation:

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.`

## PHP

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## JavaScript

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Output

`0.8063`

Time Complexity: O(N2), for calculation of mean N times while calculating Sample Standard Deviation.
Auxiliary Space: O(1), as constant extra space is required.

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