Is Calculus a requirement to become better at Probability and Satistics? Is Calculus really required to be better at Statistics and Probability and to be a good Data Scientist?
Arthur Benjamin says in his TED video:
"Very few people actually use calculus in a conscious, meaningful way in their day-to-day lives.  On the other hand, statistics–that’s a subject that you could, and should, use on a daily basis.”
“If it’s taught properly, it can be a lot of FUN. I mean, probability and statistics–it’s the mathematics of games and gambling, it’s…it’s analyzing trends, it’s predicting the future.”
 A: While I'm sure there are many on this site who will disagree, I'd like to play devil's advocate for a moment and argue that no, calculus is not really necessary to be a good applied statistician or data science person.  
It is true that advanced mathematical techniques, including calculus, are necessary to derive the mathematical theory behind statistical methods.  However, I would like to argue that in general it's not necessary to understand the math behind the statistical method in order to apply the method.  
For example, one of the most common methods applied is the t-test.  In order to use the t-test, people need to know a serious of rules regarding when it is and is not appropriate.  They do not, however, need to be able to derive the result that the t-statistic follows a t-distribution.
A: Yes, calculus is required. Statisticians must work with moments. To understand moments, you have to know calculus. It's the same with calculating tail probabilities or using maximum likelihood - you can't effectively do either in a non-textbook application without an understanding of calculus. You may not use it on a daily basis, but you will use it periodically. 
