# How to Calculate Standard Deviation through a Java program ?.

Updated on September 17, 2014

In this Java tutorial, you will learn how to calculate Standard Deviation of numbers through a simple Java program. In this tutorial, there is a Java class named as, StandardDeviationTest, having main method. This main method is the starting point of execution for any small or big Java program. In this tutorial, Standard Deviation calculation is done in main method. The method performs few steps, which are mentioned below -

## Steps to perform -

1.Create an array or list to hold few numbers, whose standard deviation is to be calculated.

2.Calculate average or mean of the numbers.

3.Calculate the difference between each number and average or mean of the numbers.

4.Take square of above calculated difference.

5.After taking squares, take sum of the squares calculated above.

6.Divide sum of squares by total numbers – 1.

7.Take square root of above division gives Standard Deviation of numbers.

Lets have look into each steps in great detail. Images below demonstrates a simple Java program which calculates Standard deviation. Each of the above steps is mentioned as points 1,2,3 etc in the images below. The complete Java source code is provided below. In this tutorial, a video is also provided, which demonstrates actual working of this program.

## Video tutorial - How to calculate Standard Deviation through a Java program.

1.Lets take few numbers say :– 23, 92, 46, 55, 63, 94, 77, 38, 84, 26, whose standard deviation is to be calculated.

2.Average or mean of the above numbers :– 59.8

3.Difference between each number and average or mean of the numbers :– -36.8, 32.2, -13.8, -4.8, 3.2, 34.2, 17.2, -21.8, 24.2, -33.8

4.Square of above calculated difference :– 1354.24, 1036.84, 190.44, 23.04, 10.24, 1169.64, 295.84, 475.24, 585.64, 1142.44.

5.Sum of the above squares :– 6283.6

6.Divide sum of squares by (total numbers – 1) :– 698.18

7.Square root gives Standard Deviation of numbers :– 26.42

```import java.util.ArrayList;
import java.util.List;

public class StandardDeviationTest {

public static void main(String[] args) {

System.out.print("Step 1 - Create list of 10 numbers as :- ");

List<Double> numbers = new ArrayList<Double>();
System.out.println("\n"+numbers);

System.out.print("\nStep 2 - Average of above 10 numbers :- ");

double sum = 0;
for(double number : numbers) {
sum = sum + number;
}

double average = sum / numbers.size();
System.out.println(sum + " / " + numbers.size()+" = " + average);

System.out.println("\nStep 3 - Difference between each number and average :- ");

List<Double> listOfDifferences = new ArrayList<Double>();

for(double number : numbers) {
double difference = number - average;
System.out.printf("%2.2f",difference);
System.out.print(" ");
}

System.out.println("\n\nStep 4 - Square of above calculated difference :- ");

List<Double> squares = new ArrayList<Double>();

for(double difference : listOfDifferences) {
double square = difference * difference;
System.out.printf("%4.2f",square);
System.out.print(" ");
}

System.out.println();
System.out.print("\nStep 5 - Sum of Squares calculated above :- ");
sum = 0;

for(double number : squares) {
sum = sum + number;
}

System.out.println(sum);

System.out.println();
System.out.print("Step 6 - Divide sum of square by total (numbers) - 1 :- ");

double result = sum / (numbers.size() - 1);

System.out.printf("%4.2f", result);

System.out.println();
System.out.println("\nStep 7 - Standard Deviation is the Square root of above result :- ");

double standardDeviation = Math.sqrt(result);

System.out.printf("%4.2f", standardDeviation);
}
}

```

## Output of the program -

Step 1 - Create list of 10 numbers as :-
[23.0, 92.0, 46.0, 55.0, 63.0, 94.0, 77.0, 38.0, 84.0, 26.0]

Step 2 - Average of above 10 numbers :- 598.0 / 10 = 59.8

Step 3 - Difference between each number and average :-
-36.80 32.20 -13.80 -4.80 3.20 34.20 17.20 -21.80 24.20 -33.80

Step 4 - Square of above calculated difference :-
1354.24 1036.84 190.44 23.04 10.24 1169.64 295.84 475.24 585.64 1142.44

Step 5 - Sum of Squares calculated above :- 6283.6

Step 6 - Divide sum of square by total (numbers) - 1 :- 698.18

Step 7 - Standard Deviation is the Square root of above result :-
26.42

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