Standard Deviation. Explain.

[Aktungbby]

^ I see it so clearly now; Jeff! You've got it in a nutshell!I didn't know air guns were so complicated.

[ikalugin]

Err you don't really need to create an object (class) for this, a simple function should do just fine.

[Jeff-Groves]

Yep. A new function is plenty good enuff. I don't like adding some monster package I'll never use.

[Eichhörnchen]

Nothing worse than having a monster package and never using it.

[Pisces]

I have never understood why it has to divide by N-1. Can anyone explain why it is less 1?

I mean, simple averages are simply the sum divided by N. That makes sense to spread the (sum of) differences accross all samples.

[Tango589]

Originally Posted by Eichhornchen

Nothing worse than having a monster package and never using it.

Fnaar, fnaar.

[vienna]

You know, when I saw the title of this thread, I was a bit confused. I live in Hollywood, California; here, a standard deviation is anything that does not require above normal medical attention, a lengthy session in a confessional, or an excessive bail...


<O>

[Chad]

I am a bit rusty on my C++, but maybe we can get you going in the right direction with some psuedo-code!

We know we will have a list of items with numeric values, for simplicity sake, let's assume these are doubles.

So, let's pass that to stubbed method:

public void CalculateStandardDev(double listOfDoubles)
{

}

Now, we know the length of our array using the following:

listOfDoubles.size();

This will be our 'n' variable

public void CalculateStandardDev(double listOfDoubles)
{
     int sizeOfList = listOfDoubles.size();
}

Now we can find the mean by adding an additional local parameter called temporarySum and adding to it while in scope. This may be where my C++ rusty-ness shows

public void CalculateStandardDev(double listOfDoubles)
{
     int sizeOfList = listOfDoubles.size();
     double temporarySum = 0;

     for(int i=0; i<sizeOfList; i++)
     {
         temporarySum += listOfDoubles[i];
     }
}

[Chad]

Sorry, was scared I was going to lose progress.. Anyways, now we have the sum of all of our items and our 'n' variable. But we still don't have the mean, or the average. So.. to find the average we divide the sum of all of our numbers by 'n', our size of our list:

public void CalculateStandardDev(double listOfDoubles)
{
     int sizeOfList = listOfDoubles.size();
     double temporarySum = 0;

     for(int i=0; i<sizeOfList; i++)
     {
         temporarySum += listOfDoubles[i];
     }

     double averageOfList = temporarySum / sizeOfList;
}

Done with Step 1!

So now we go into Step 2, which has this equation:



We look at each value and subtract the mean and square the result. Sounds easy enough:

public void CalculateStandardDev(double listOfDoubles)
{
     int sizeOfList = listOfDoubles.size();
     double temporarySum = 0;

     for(int i=0; i<sizeOfList; i++)
     {
         temporarySum += listOfDoubles[i];
     }

     double averageOfList = temporarySum / sizeOfList;

     for(int j=0; j<sizeOfList; j++)
     {
         listOfDoubles[j] = pow(listOfDoubles[j] - averageOfList, 2);
     }
}

What I am doing is replacing the original value from the list with the calculated result of that value minus the average, and using the pow method to square the result. Square being to the second power.

pow(number, exponentValue)

Now we will loop through our list again and add the new listOfDoubles to eachother, or from 1 to N, N being our variable sizeOfList. We then need to divide by our size of list to give us, VARIANCE!

public void CalculateStandardDev(double listOfDoubles)
{
     int sizeOfList = listOfDoubles.size();
     double temporarySum = 0;

     for(int i=0; i<sizeOfList; i++)
     {
         temporarySum += listOfDoubles[i];
     }

     double averageOfList = temporarySum / sizeOfList;

     for(int j=0; j<sizeOfList; j++)
     {
         listOfDoubles[j] = pow(listOfDoubles[j] - averageOfList, 2);
     }

    double squaredDifference = 0;
    double variance = 0;

    for(int k=0; k<sizeOfList; k++)
   {
         squaredDifference += listOfDoubles[k];
   }

   variance = squaredDifference / sizeOfList;
}

[Chad]

Now that we have our variance, the last step is extremely easy. We simply take the square root of variance to give us the Standard Deviation value!!!

public double CalculateStandardDev(double listOfDoubles)
{
     int sizeOfList = listOfDoubles.size();
     double temporarySum = 0;

     for(int i=0; i<sizeOfList; i++)
     {
         temporarySum += listOfDoubles[i];
     }

     double averageOfList = temporarySum / sizeOfList;

     for(int j=0; j<sizeOfList; j++)
     {
         listOfDoubles[j] = pow(listOfDoubles[j] - averageOfList, 2);
     }

    double squaredDifference = 0;
    double variance = 0;

    for(int k=0; k<sizeOfList; k++)
   {
         squaredDifference += listOfDoubles[k];
   }

   variance = squaredDifference / sizeOfList;

   double standardDeviationValue = sqrt (variance );
   return standardDeviationValue;
}

[Skybird]

Brrr, take it away, it hurts our eyes! Last time I did stuff like that, was in GFA 3.0 on an Amiga, 25 years ago.

[Jeff-Groves]

I'm gonna go with C++ Mathematical Expression Toolkit Library (ExprTk).
It's a neat header file I can use then throw away along with those old Dewalt side cuts.

[Chad]

Originally Posted by Jeff-Groves

I'm gonna go with C++ Mathematical Expression Toolkit Library (ExprTk).
It's a neat header file I can use then throw away along with those old Dewalt side cuts.

Well it was fun going back and writing that method

[Armistead]

I had a deviated septum once.

[Red October1984]

Originally Posted by Skybird

Started statistics courses?

I've got this stuff in Psychology right now. It's in a chapter about mental retardation and how common and how severe it is.