Question

Exercise 5.46 computes the standard deviation of numbers. This exercise uses a different but equivalent formula to compute the standard deviation of n numbers. To compute the standard deviation with this formula, you have to store the individual numbers using a list, so that they can be used after the mean is obtained. Your program should contain the following functions:

Compute the standard deviation of values def deviation(x) Compute the mean of a list of values def mean (x) write a test program that prompts the user to enter a list of numbers and displays the mean and standard deviation, as shown in the following sample run Programming Exercises 351 Enter numbers: 1.9 2.5 3.7 2 1 6 3 4 5 2 FEner The mean is 3.11 The standard deviation is 1.55738

Answer 1

// This program is written in Java Programming Language

// Comments are used for explanatory purpose

// Program starts here

import java.util.Scanner;

public class STDeviation {

// Declare and Initialise size of Numbers to be 10

int Numsize = 10;

public static void main(String args [] ) {

Scanner scnr = new Scanner(System.in);

// Declare digits as double

double[] digits = new double[Numsize];

System.out.print("Enter " + Numsize + " digits: ");

// Input digits using iteration

for (int i = 0; i < digits.length; i++)

{

digits[i] = scnr.nextDouble();

}

// Calculate and Print Mean/Average

System.out.print("Average: " + mean(digits)+'\\');

// Calculate and Print Standard Deviation

System.out.println("Standard Deviation: " + deviation(digits));

}

// Standard Deviation Module

public static double deviation(double[] x) {

double mean = mean(x);

// Declare and Initialise deviation to 0

double deviation = 0;

// Calculate deviation

for (int i = 0; i < x.length; i++) {

deviation += Math.pow(x[i] - mean, 2);

}

// Calculate length

int len = x.length - 1;

return Math.sqrt(deviation / len);

}

// Mean Module

public static double mean(double[] x) {

// Declare and Initialise total to 0

double total = 0;

// Calculate total

for (int i = 0; i < x.length; i++) {

total += x[i];

}

// Calculate length

int len = x.length;

// Mean = total/length

return total / len;

}

}