Admission
Only one test score needs to be above the threshold on either of the Cattell tests to gain entry into the Mensa Institute.
I was 1 point off acceptance with a score of 131 as the top 97.3% rather than 97.5%. As admission rounds up to the 98% threshold.
So a score of 132 for a .16 standard deviation (SD) is the cutoff for entry of 97.72% which is a roundup from 97.5% to 98% within the scores of the total human population.
IQ tests generally take multiple times to gain a perfect representative score. Depending on the test will be how many times you need to do it.
This variance is called a confidence interval, standard error of measurement or reliability score.
Reliability studies of the Cattell Culture Fair IQ test indicate that it hovers around .75 to 0.92.
I only did the test once. So if I took the test again, it is extremely likely I would gain at least 1 IQ point and be admitted into Mensa. It's on my bucket list of things to do.
Retaking the test in Australia is very expensive with a psychologist. This website quotes between "$1500 and $2100" AUD, this website $990, as common examples. As the psych needs specialised training.
Mensa in Australia only runs tests infrequently compared to the UK and doesn't offer the Cattell as an option. There are a handful of main IQ tests (WAIS, Stanford, etc).
Mensa USA offers both the Cattell and it's own test. Mensa UK offers the Cattell (CFIT-III) as the standard main test.
So I decided that it's just better to combine the test with a holiday when the time arrives.
So I will resit the test at some point when I go back to the UK where its only £25 to do the test, or the US which is $60-$100.