# Computing the standard deviation of a Number array in Java

(See the next iteration.)

I have this funky class method for computing standard deviation from an array of Number objects using the Stream API:

StandardDeviation.java:

package net.coderodde.util;

import java.util.Arrays;

public class StandardDeviation {

public static double computeStandardDeviation(Number... collection) {
if (collection.length == 0) {
return Double.NaN;
}

final double average =
Arrays.stream(collection)
.mapToDouble((x) -> x.doubleValue())
.summaryStatistics()
.getAverage();

final double rawSum =
Arrays.stream(collection)
.mapToDouble((x) -> Math.pow(x.doubleValue() - average,
2.0))
.sum();

return Math.sqrt(rawSum / (collection.length - 1));
}

public static void main(String[] args) {
// Mix 'em all!
double sd = computeStandardDeviation((byte) 1,
(short) 2,
3,
4L,
5.0f,
6.0);

System.out.println(sd);
}
}


Please, tell me anything that comes to mind.

That's a nice and clean, short piece of code. :) It also appears to calculate the result correctly. My observations will follow, but really, only the first one is actually an issue:

• The application will crash with a NullPointerException if you try to compute the standard deviation for null. In addition to checking collection.length == 0, you should first check for collection == null.
• You should be consistent with your use of the final modifier. Finalize that Number... collection, String[] args and double sd too.
• While at it, you could finalize the entire class as well and add an empty private constructor: private StandardDeviation() { /* prevent instantiation */ }. It's an utility class with only static methods, so you don't need anyone calling new StandardDeviation() as it currently stands. Some static code analyzers would actually point this out as a minor issue for you.
• Personally I find the use of method references nice and clear, so you could replace .mapToDouble((x) -> x.doubleValue()) with .mapToDouble(Number::doubleValue)
• I find that .mapToDouble((x) -> Math.pow(x.doubleValue() - average, 2.0)) does too much at once, you could also do it like this instead: .mapToDouble(Number::doubleValue).map(x -> x - average).map(StandardDeviation::square) and then you'd have a new method like this in your class: private static Double square(final Double value) { return Math.pow(value, 2.0); }. At least the Math.pow(...) part is much easier to read as a method reference.
• As an external user of your utility class I'd like the option to call the standard deviation method with a Collection instead of varargs parameters. You'd then have to make one of the methods to call the other, first converting either the array into a collection or the other way around. Personally I prefer working with Collections.
• You are traversing the collection twice to determine the standard deviation when you could do it in a single pass.
• Also, you could accumulate quickly rounding errors with the Math.pow(x.doubleValue() - average, 2.0) call. It would be best to implement the Kahan summation algorithm (that the Stream API has for DoubleStream#sum()).
• In the lambda expression (x) -> x.doubleValue(), you don't need to add the parentheses around (x). You can just have x -> x.doubleValue(). You could also use a method-reference, which avoids a lamda, and have Number::doubleValue.

On Stack Overflow, I wrote an answer which calculates the standard deviation in a single pass with compensation. It is parallel-friendly:

static class DoubleStatistics extends DoubleSummaryStatistics {

private double sumOfSquare = 0.0d;
private double sumOfSquareCompensation; // Low order bits of sum
private double simpleSumOfSquare; // Used to compute right sum for
// non-finite inputs

@Override
public void accept(double value) {
super.accept(value);
double squareValue = value * value;
simpleSumOfSquare += squareValue;
sumOfSquareWithCompensation(squareValue);
}

public DoubleStatistics combine(DoubleStatistics other) {
super.combine(other);
simpleSumOfSquare += other.simpleSumOfSquare;
sumOfSquareWithCompensation(other.sumOfSquare);
sumOfSquareWithCompensation(other.sumOfSquareCompensation);
return this;
}

private void sumOfSquareWithCompensation(double value) {
double tmp = value - sumOfSquareCompensation;
double velvel = sumOfSquare + tmp; // Little wolf of rounding error
sumOfSquareCompensation = (velvel - sumOfSquare) - tmp;
sumOfSquare = velvel;
}

public double getSumOfSquare() {
double tmp = sumOfSquare + sumOfSquareCompensation;
if (Double.isNaN(tmp) && Double.isInfinite(simpleSumOfSquare)) {
return simpleSumOfSquare;
}
return tmp;
}

public final double getStandardDeviation() {
long count = getCount();
double sumOfSquare = getSumOfSquare();
double average = getAverage();
return count > 0 ? Math.sqrt((sumOfSquare - count * Math.pow(average, 2)) / (count - 1)) : 0.0d;
}

public static Collector<Double, ?, DoubleStatistics> collector() {
return Collector.of(DoubleStatistics::new, DoubleStatistics::accept, DoubleStatistics::combine);
}

}


It has the same logic as DoubleSummaryStatistics but extended to calculate the sum of squares.

With such a class, you can then have:

public static double computeStandardDeviation(Number... collection) {
return Arrays.stream(collection)
.map(Number::doubleValue)
.collect(DoubleStatistics.collector())
.getStandardDeviation();
}

• You are very knowledgeable about Java's APIs. Commented Apr 29, 2018 at 8:41
• This version calculates the standard deviation as count > 0 ? Math.sqrt((sumOfSquare - count * Math.pow(average, 2)) / (count - 1)) : 0.0d; but the version you link to on StackOverflows has getCount() > 0 ? Math.sqrt((getSumOfSquare() / getCount()) - Math.pow(getAverage(), 2)) : 0.0d; Are they equivalent? Commented Jan 3, 2023 at 12:15