Example 4.4 Computing Mean and Standard Deviations

In this example, you will write a program that generates 10 random numbers and computes the mean and standard deviations of these numbers using the following formula:

A sample run of the following program is shown in Figure 4.8.

// ComputeMeanDeviation.java: Demonstrate using the math methods

public class ComputeMeanDeviation

{

  /**Main method*/

  public static void main(String[] args)

  {

    final int count = 10; // Total numbers

    int number = 0; // Store a random number

    double sum = 0; // Store the sum of the numbers

    double squareSum = 0; // Store the sum of the squares   

    // Create numbers, find its sum, and its square sum

    for (int i=0; i<count; i++)

    {

      // Generate a new random number

      number = (int)Math.round(Math.random()*1000);

      System.out.println(number);

      // Add the number to sum

      sum += number;

      // Add the square of the number to squareSum

      squareSum += Math.pow(number, 2); // Same as number*number;

    }

    // Find mean

    double mean = sum/count;

    // Find standard deviation

    double deviation = Math.sqrt((squareSum - sum*sum/count)/(count - 1));

    // Display result

    System.out.println("The mean is " + mean);

    System.out.println("The standard deviation is " + deviation);

  }

}      

Figure 4.8

The program finds the mean and standard deviations of 10 random integers.

Example Review

The program demonstrates the use of the math methods random, round, pow, and sqrt. The random method generates a double value that is greater than or equal to 0 and less than 1.0. After multiplying the generated number by 1000, the random number is greater than or equal to 0 and less than 1000.0. The round method converts the double number into a long value, which is cast into an int variable number.

Invoking pow(number, 2) returns the square of number. The sqrt method is used to get the square root of a double value. 

The formula for computing standard deviation used in the example is equivalent to the following formula:

To use this formula, you have to store the individual numbers using an array so that they can be used after the mean is obtained.