How can I test private members and methods of classes?

I am trying to do unit testing (using the Boost unit testing framework) on a C++ class called VariableImpl. Here are the details.

class Variable
{
public:
  void UpdateStatistics (void) {
    // compute mean based on m_val and update m_mean;
    OtherClass::SendData (m_mean);
    m_val.clear ();
  }
  virtual void RecordData (double) = 0;

protected:
  std::vector<double> m_val;

private:
  double m_mean;
};

class VariableImpl : public Variable
{
public:
  virtual void RecordData (double d) {
    // Put data in m_val
  }
};

How can I check that the mean is computed correctly? Note that 1) m_mean is protected and 2) UpdateStatistics calls a method of another class and then clears the vector.

The only way I can see would be to add a getter (for instance, GetMean), but I don't like this solution at all, nor I think it is the most elegant.

How should I do?

And what should I do if I were to test a private method instead of a private variable?