I am better than %

[linus1]

Hi,

I want to calculate how many people (%) I am better than...

SD=0.025
N (people) = 20
X (average) = 7.5

My average is 8.

I want to know how many percent I am likely to be better than compare to N .

 

[Karabiner]

It depends on the shape of the distribution.

 

[fed2]

also depends on what is meant by 'better'. Could be smaller values are 'better'.

 

[linus1]

Thanks,
It is a item rating (1-10).
Symetric distribution.
I want to know how many percent of items, item Y is better than.
"This item is better than 50% of other items".

 

[AngleWyrm]

Z-Scores can be used to answer the question "What is the probability an observation is greater/less than some value x"
Which can also be presented as "What proportion of the outcomes is greater/less than some value x"
Whichever version seems to make the most sense to the researcher for the problem at hand.

Here's an easy to follow video tutorial on Z-scores

In the example given, the observation value of 8 or more is extremely unlikely, being approximately 1 in 2.7x10^89, which is several orders of magnitude larger than an estimate of the number of atoms in the universe.