Super class knowing the type of its children? Surely there is a better way
First, I get some error messages when I put this in the compiler.
I had to replace the anonymous inner class that is returned by performAnalysis with a helper class. I'm not a fan of helper classes like this, so it would be nice if someone else had a better idea.

Second, I'm thinking generics would solve this quite nicely.
I agree that the parent class should not need to know it's child classes, but it can obtain this data; see the methods that I have commented out. I have commented them out because I don't like them, but still want to show that it's possible. I'll admit that using .class is a bit tricky when using generics, because of type erasure. However, as long as the generic types are known at compile time, this should not be a problem.

interface IDataAnalysis&lt;InputType extends IAnalysisData, OutputType extends IAnalysisData&gt; {

//    public Class&lt;?&gt; getInputDataType( );
//    public Class&lt;?&gt; getOutputDataType( );

    OutputType performAnalysis(InputType inputData);
}

public class DataAnalysisMean implements IDataAnalysis&lt;IAnalysisDataSet, IAnalysisDataScalar&gt; {

//    
//    public Class&lt;?&gt; getInputDataType( ) { return IAnalysisDataSet.class; }
//    public Class&lt;?&gt; getOutputDataType( )  { return IAnalysisDataScalar.class; }

public IAnalysisDataScalar performAnalysis(IAnalysisDataSet inputData) {

    IAnalysisDataSet inputDataSet = (IAnalysisDataSet)inputData;
    double sum = 0;

    for (int i = 0; i &lt; inputDataSet.getCount(); i++) {
        IAnalysisData dataItem = inputDataSet.getData(i);
        IAnalysisDataScalar dataItem2 = (IAnalysisDataScalar)dataItem;
        sum += dataItem2.getValue();
    }

    return new HelperClass( inputDataSet, sum );
}

private class HelperClass implements IAnalysisDataScalar
{
    IAnalysisDataSet inputDataSet;
    double sum = 0;

    HelperClass( IAnalysisDataSet inputSet, double sum )
    {
        this.inputDataSet = inputSet;
        this.sum = sum; 
    }

    @Override
    public double getValue() {
        return sum / inputDataSet.getCount();
    }

    @Override
    public AnalysisDataType getType() {
        return AnalysisDataType.Scalar;
    }
   }
}