Reasons for Z-Score standard deviation ? 1???

rheighton

New member
Joined
Mar 16, 2006
Messages
11
I have a series of 24 raw scores which I have standardized by individually converting them to z-scores. My assignment asks me to calculate the mean and standard deviation of these new scores (I presume to prove that the mean for a series of z-scores is always = 0 and the standard deviation for a series of z-scores is always = 1).

As expected, the mean of the scores (which ranged from -1.79 to 1.33) = 0. However, upon calculating the standard deviation for the series of scores, I am getting 0.84 as the value (which is clearly incorrect). I have run through my math thrice to ensure that I didn't make a simple calculation error, so I cannot understand why my standard deviation would not come out as = 1.

I am using the formula:

SD = ?( [ ?z^2 – (?z)^2/N ] / N )
where (?z)^2 = 0 and N = 24
Reducing the formula to:
SD = ?( [?z^2] / N )

And in calculating ?z^2 I added the squares of each individual z-score (giving me a value of ~16.74).

If anyone could possibly give me a heads up as to where I went wrong (or perhaps suggesting other reasons why the SD wouldn't = 1) it would be GREATLY appreciated!
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,790
You are right to suspect such a result.

I still believe there is something wrong in your calculations. It is rather tedious. Are you using a spreadsheet or are we talking paper and pencil?

Provide data and results. Someone will find the error. It's in there.
 

rheighton

New member
Joined
Mar 16, 2006
Messages
11
Thanks very much for your reply. I actually figured out that I had made a small oversight in an earlier calculation which skewed the rest of my results... easy enough to do when calculating with paper and pencil!
 
Top