Given a class interval and frequency of the class and the task is to find standard deviation of grouped data.
Formula to find standard deviation
Standard Deviation = ?( (?(F x M2 – n x ?2)) / (n-1) )
Where,
F – frequency of the class.
M – mid value of class interval.
? – Mean of the grouped data.
n – sum of frequency.
Examples:
Input : lower_limit[] = {50, 61, 71, 86, 96}
upper_limit[] = {60, 70, 85, 95, 100}
freq[] = {9, 7, 9, 12, 8}
Output : 15.757
Explanation :
Standard deviation = sqrt(287127.75 - 45 *
78.3444 * 78.3444) / (45 - 1)
= 15.757
Input : lower_limit[] = {37, 47, 57, 67}
upper_limit[] = {46, 56, 66, 76}
freq[] = {19, 23, 27, 28}
Output : 10.9817
CPP
// CPP Program to implement standard // deviation of grouped data.#include <bits/stdc++.h>using namespace std;
// Function to find mean of grouped data.float mean(float mid[], int freq[], int n)
{ float sum = 0, freqSum = 0;
for (int i = 0; i < n; i++) {
sum = sum + mid[i] * freq[i];
freqSum = freqSum + freq[i];
}
return sum / freqSum;
}// Function to find standard// deviation of grouped data.float groupedSD(float lower_limit[],
float upper_limit[],
int freq[], int n)
{ float mid[n], sum = 0, freqSum = 0, sd;
for (int i = 0; i < n; i++) {
mid[i] = (lower_limit[i] + upper_limit[i]) / 2;
sum = sum + freq[i] * mid[i] * mid[i];
freqSum = freqSum + freq[i];
}
// Formula to find standard deviation
// of grouped data.
sd = sqrt((sum - freqSum * mean(mid, freq, n) *
mean(mid, freq, n)) / (freqSum - 1));
return sd;
}// Driver function.int main()
{ // Declare and initialize
// the lower limit of interval.
float lower_limit[] = { 50, 61, 71, 86, 96 };
// Declare and initialize
// the upper limit of interval.
float upper_limit[] = { 60, 70, 85, 95, 100 };
int freq[] = { 9, 7, 9, 12, 8 };
// Calculating the size of array.
int n = sizeof(lower_limit) / sizeof(lower_limit[0]);
cout << groupedSD(lower_limit, upper_limit, freq, n);
return 0;
} |
Java
// Java program to implement // standard deviation of grouped data.import java.io.*;
class GFG {
// Function to find mean of grouped data.
static float mean(float mid[], int freq[], int n)
{
float sum = 0, freqSum = 0;
for (int i = 0; i < n; i++)
{
sum = sum + mid[i] * freq[i];
freqSum = freqSum + freq[i];
}
return sum / freqSum;
}
// Function to find standard
// deviation of grouped data.
static float groupedSD(float lower_limit[],
float upper_limit[],
int freq[], int n)
{
float mid[] = new float[n];
float sum = 0, freqSum = 0, sd;
for (int i = 0; i < n; i++)
{
mid[i] = (lower_limit[i] + upper_limit[i]) / 2;
sum = sum + freq[i] * mid[i] * mid[i];
freqSum = freqSum + freq[i];
}
// Formula to find standard deviation
// deviation of grouped data.
sd = (float)Math.sqrt((sum - freqSum * mean(mid, freq, n) *
mean(mid, freq, n)) / (freqSum - 1));
return sd;
}
// Driver function.
public static void main (String[] args)
{
// Declare and initialize
// the lower limit of interval.
float lower_limit[] = { 50, 61, 71, 86, 96 };
// Declare and initialize
// the upper limit of interval.
float upper_limit[] = { 60, 70, 85, 95, 100 };
int freq[] = { 9, 7, 9, 12, 8 };
// Calculating the size of array.
int n = lower_limit.length;
System.out.println( groupedSD(lower_limit,
upper_limit, freq, n));
}
}// This code is contributed by vt_m |
Python3
# Python Program to implement standard# deviation of grouped data.import math
# Function to find mean of grouped data.def mean( mid, freq, n):
sum = 0
freqSum = 0
for i in range(0,n):
sum = sum + mid[i] * freq[i]
freqSum = freqSum + freq[i]
return sum / freqSum
# Function to find standard# deviation of grouped data.def groupedSD(lower_limit, upper_limit ,freq , n):
mid=[[0] for i in range(0,n)]
sum = 0
freqSum = 0
sd=0
for i in range(0,n):
mid[i] = (lower_limit[i] + upper_limit[i]) / 2
sum = sum + freq[i] * mid[i] * mid[i]
freqSum = freqSum + freq[i]
# Formula to find standard deviation
# of grouped data.
sd = math.sqrt((sum - freqSum * mean(mid, freq, n)* mean(mid, freq, n)) / (freqSum - 1))
return sd
# driver code# Declare and initialize# the lower limit of interval.lower_limit= [ 50, 61, 71, 86, 96 ]
# Declare and initialize# the upper limit of interval.upper_limit= [ 60, 70, 85, 95, 100 ]
freq =[ 9, 7, 9, 12, 8 ]
# Calculating the size of array.n = len(lower_limit)
print(groupedSD(lower_limit, upper_limit, freq, n))
# This code is contributed by Gitanjali. |
C#
// C# program to implement // standard deviation of grouped data.using System;
class GFG {
// Function to find mean of grouped data.
static float mean(float []mid, int []freq,
int n)
{
float sum = 0, freqSum = 0;
for (int i = 0; i < n; i++)
{
sum = sum + mid[i] * freq[i];
freqSum = freqSum + freq[i];
}
return sum / freqSum;
}
// Function to find standard
// deviation of grouped data.
static float groupedSD(float []lower_limit,
float []upper_limit,
int []freq, int n)
{
float []mid = new float[n];
float sum = 0, freqSum = 0, sd;
for (int i = 0; i < n; i++)
{
mid[i] = (lower_limit[i] + upper_limit[i]) / 2;
sum = sum + freq[i] * mid[i] * mid[i];
freqSum = freqSum + freq[i];
}
// Formula to find standard deviation
// deviation of grouped data.
sd = (float)Math.Sqrt((sum - freqSum * mean(mid,
freq, n) * mean(mid, freq, n)) / (freqSum - 1));
return sd;
}
// Driver function.
public static void Main ()
{
// Declare and initialize
// the lower limit of interval.
float []lower_limit = { 50, 61, 71, 86, 96 };
// Declare and initialize
// the upper limit of interval.
float []upper_limit = { 60, 70, 85, 95, 100 };
int []freq = { 9, 7, 9, 12, 8 };
// Calculating the size of array.
int n = lower_limit.Length;
Console.WriteLine(groupedSD(lower_limit,
upper_limit, freq, n));
}
}// This code is contributed by vt_m |
PHP
<?php// PHP Program to implement standard // deviation of grouped data.// Function to find mean of grouped data.function mean($mid, $freq, $n)
{ $sum = 0; $freqSum = 0;
for ( $i = 0; $i <$n; $i++)
{
$sum = $sum + $mid[$i] *
$freq[$i];
$freqSum = $freqSum + $freq[$i];
}
return $sum / $freqSum;
}// Function to find standard// deviation of grouped data.function groupedSD($lower_limit,
$upper_limit,
$freq, $n)
{ $mid=array(); $sum = 0;
$freqSum = 0; $sd;
for ( $i = 0; $i < $n; $i++)
{
$mid[$i] = ($lower_limit[$i] +
$upper_limit[$i]) / 2;
$sum = $sum + $freq[$i] *
$mid[$i] * $mid[$i];
$freqSum = $freqSum + $freq[$i];
}
// Formula to find standard deviation
// of grouped data.
$sd = sqrt(($sum - $freqSum *
mean($mid, $freq, $n) *
mean($mid, $freq, $n)) /
($freqSum - 1));
return $sd;
} // Driver Code
// Declare and initialize
// the lower limit of interval.
$lower_limit = array(50, 61, 71, 86, 96);
// Declare and initialize
// the upper limit of interval.
$upper_limit = array(60, 70, 85, 95, 100);
$freq = array( 9, 7, 9, 12, 8 );
// Calculating the size of array.
$n = count($lower_limit);
echo groupedSD($lower_limit, $upper_limit,
$freq, $n);
// This code is contributed by anuj_67.?> |
Javascript
<script>// JavaScript program to implement // standard deviation of grouped data. // Function to find mean of grouped data.
function mean(mid, freq, n)
{
let sum = 0, freqSum = 0;
for (let i = 0; i < n; i++)
{
sum = sum + mid[i] * freq[i];
freqSum = freqSum + freq[i];
}
return sum / freqSum;
}
// Function to find standard
// deviation of grouped data.
function groupedSD(lower_limit,
upper_limit,
freq, n)
{
let mid = [];
let sum = 0, freqSum = 0, sd;
for (let i = 0; i < n; i++)
{
mid[i] = (lower_limit[i] + upper_limit[i]) / 2;
sum = sum + freq[i] * mid[i] * mid[i];
freqSum = freqSum + freq[i];
}
// Formula to find standard deviation
// deviation of grouped data.
sd = Math.sqrt((sum - freqSum * mean(mid, freq, n) *
mean(mid, freq, n)) / (freqSum - 1));
return sd;
}
// Driver code // Declare and initialize
// the lower limit of interval.
let lower_limit = [50, 61, 71, 86, 96];
// Declare and initialize
// the upper limit of interval.
let upper_limit = [ 60, 70, 85, 95, 100 ];
let freq = [ 9, 7, 9, 12, 8];
// Calculating the size of array.
let n = lower_limit.length;
document.write( groupedSD(lower_limit,
upper_limit, freq, n));
</script> |
Output:
15.757
Time Complexity: O(n)
Auxiliary Space: O(n)