Standard Deviation

What the hell is standard deviation anyway?

Well I wrote a prog to calculate the mean and standard devation of a set of numbers. The mean part was easy enough but I'm having probs with the standard deviation. Here is the code I'm using:

VB Code:

Dim X As Long
Dim SumX1 As Single
Dim SumX2 As Single
Dim NumValues As Integer
 
'Seperate Numbers'
Array1 = Split(txtNumbers.Text, ",")
    
Total = 0
For X = 0 To UBound(Array1)
    Total = Total + Array1(X)
Next X
 
SumX1 = SumX1 + Total
SumX2 = SumX2 + Total ^ 2
NumValues = UBound(Array1) + 1
 
'Calculate and Display Mean
Mean = SumX1 / NumValues
lblMean.Caption = Mean
 
'Calculate and Display Standard Deviation
Stdev = Sqr((NumValues * SumX2 - SumX1 ^ 2) / (NumValues * (NumValues - 1)))
 
lblDeviation.Caption = Stdev

I'm not getting the right answer for the standard deviation. So maybe one of you brainy guys could tell me where I've gone wrong.

VB Code:

Dim X As Long
Dim SumX1 As Single
Dim SumX2 As Single
Dim NumValues As Integer
 
'Seperate Numbers'
Array1 = Split(txtNumbers.Text, ",")
    
Total = 0
For X = 0 To UBound(Array1)
    Total = Total + Array1(X)
Next X
 
SumX1 = SumX1 + Total
'not needed SumX2 = SumX2 + Total ^ 2
NumValues = UBound(Array1) + 1
 
'Calculate and Display Mean
Mean = SumX1 / NumValues
lblMean.Caption = Mean
 
'Calculate and Display Standard Deviation
for X=1 to NumValues
    SumX2=(Array1(X)-Mean)*(Array1(X)-Mean)
next X
Stdev=Sqr(SumX2/(NumValues-1)
lblDeviation.Caption = Stdev

'I got that from German Explantion

yeah, Standard Deviation must be worked out Term-by-term, finiding the deviation of each term from the mean, squaring it, ading these squares up and finding the square root.

Just a change to the code by opus:

VB Code:

'SumX2=(Array1(X)-Mean)*(Array1(X)-Mean)
'should be
SumX2=SumX2 + (Array1(X)-Mean)^2

I think this is needed, otherwise the sum at the end is just the (deviation of the last value from the mean) squared.

Think of standard deviation as how spread out a frequency distribution curve is. This curve is the famous 'bell-shaped' curve.

If the curve has steep sides (narrow) the std dev is small.
IF the sides are spread out, the std is large.
std dev is called 'sigma', and 95% of the population lies within the area under the curve defined by:

( mean +/- 2 * sigma).

Standard deviation is a way to see if one data set, for example= height measurements, is a part of the population.

In plain English, you use it to find if your measurements match another group of measurements or not.