Calculate Standard Deviation in Java

In this article, we will understand how to calculate standard deviation. The standard deviation is the measure of how spread-out numbers are. The symbol of standard deviation is sigma( σ ). It is the square root of variance.

Standard deviation is computed using the formula square root of ∑(Xi - ?)2 / N where Xi is the element of the array, ? is mean of the elements of the array, N is the number of elements, ∑ is the sum of the each element.

Problem Statement

Given a program in Java to calculate the standard deviation of a given array of numbers, with the option to either input the array values manually or use a predefined array.

Input

Input Array : [ 35.0, 48.0, 60.0, 71.0, 80.0, 95.0, 130.0 ]

Output

Standard Deviation: 29.313227

Steps to Calculate Standard Deviation

Below are the steps to calculate standard deviation −

• Step 1: START
• Step 2: Declare a double array namely input_array, two doube values namely sum and standard_deviation.
• Step 3: Read the required values from the user/ define the values.
• Step 4: Compute ∑(Xi - ?)2 / N and store the value in result variable.
• Step 5: Display the result
• Step 6: Stop

Example 1

Here, the input is being entered by the user based on a prompt.

public class StandardDeviation {
   public static void main(String[] args) {
      double[] input_array = { 35, 48, 60, 71, 80, 95, 130};
      System.out.println("The elements of the array is defined as");
      for (double i : input_array) {
         System.out.print(i +" ");
      }
      double sum = 0.0, standard_deviation = 0.0;
      int array_length = input_array.length;
      for(double temp : input_array) {
         sum += temp;
      }
      double mean = sum/array_length;
      for(double temp: input_array) {
         standard_deviation += Math.pow(temp - mean, 2);
      }
      double result = Math.sqrt(standard_deviation/array_length);
      System.out.format("\n\nThe Standard Deviation is: %.6f", result);
   }
}

Output

The elements of the array is defined as
35.0 48.0 60.0 71.0 80.0 95.0 130.0

The Standard Deviation is: 29.313227

Example 2

Here, we have defined a function to compute standard deviation.

public class StandardDeviation {
public static void main(String[] args) {
      double[] input_array = { 35, 48, 60, 71, 80, 95, 130};
      System.out.println("The elements of the array is defined as");
      for (double i : input_array) {
         System.out.print(i +" ");
      }
      double standard_deviation = calculateSD(input_array);
      System.out.format("\n\nThe Standard Deviation is: %.6f", standard_deviation);
   }
   public static double calculateSD(double input_array[]) {
      double sum = 0.0, standard_deviation = 0.0;
      int array_length = input_array.length;
      for(double temp : input_array) {
         sum += temp;
      }
      double mean = sum/array_length;
      for(double temp: input_array) {
         standard_deviation += Math.pow(temp - mean, 2);
      }
      return Math.sqrt(standard_deviation/array_length);
   }
}

Output

The elements of the array is defined as
35.0 48.0 60.0 71.0 80.0 95.0 130.0

The Standard Deviation is: 29.313227