way of measuring standard scores
(this is the basic
standard score); often used on psychological tests
To calculate the Z score from a raw score
out of a set
, use this formula
Z=(X-MX) ÷ s
Where X = the raw score you want to convert,
MX = the mean of X, as is standard, and
s = the standard deviation, as is also standard, as it were.
For example, let's say a group of level 3 Everthingians created the following number of writeups since joining:
and wanted to find the Z score for one of the people who'd written 94, you would find out the standard deviation and mean (much like a cooking show, I've already prepared these for you: 5.9 and 87.5, respectively) and then work out this equation:
Z = (94 - 87.5) ÷ 5.9
Which, as you can see, equals 1.1; that's your Z score.
So what does it mean? The Z score tells you how far you are from the mean in terms of standard deviation, where the mean equals 0 and each standard deviation away from it is one integer away from the mean.
If you don't like these pesky decimals and aren't familiar enough with the normal curve to be able to imagine just what a score of 1.1 or -3.9 means, you can convert your z score to a t score, which may be easier to wrap one's mind around.