None of the above answers make any physical sense. Why should I look for maximal variance really? Intuitively isn’t more variance means more noise? Wish some sensible person who is trained to think and not regurgitate mathematics jingo would have said “we are looking for a variable that is responsible for an observation ie its values are correlated in some sense to observation like variable ‘quantity of sugar’ to observation ‘diabetes’. So more the observations you make, more is the variability because some eat less sugar, some more and not everyone who eats more sugar is necessarily diabetic. But there is definitely a correlation. But if sugar was not responsible for diabetes and if I sample thousands of people how would the data look? Variance of observable makes no sense