Possible Rule of thumb for sums of variances?

The sum of independent r.v.'s is not $50$ times one of them. So the variance properties are that if $X_1,ldots,X_n$ are independent (or pairwise uncorrelated) then $$ text{Var}(X_1+ldots+X_n)=text{Var}(X_1)+ldots+text{Var}(X_n). $$ So for $50$ identically distributed and independent summands it will be $50text{Var}(X_1)$.

Multiplying by 50 the variance of one variabile or summing the same variance of 50 variabiles is not the same thing.

$V[50X]=50^2V[X]$

But if $X_i stackrel{d}=X_j$

(All the random variabiles have the same distribution and thus also the same variance, say $V[X]$)

$V[X_1+X_2+...+X_{50}]=50V[X]$

This, IF THE RV'S ARE UNCORRELATED. Otherwise you must sum all the covariances.

$$V[sum_i X_i]=sum_i sum_j Cov(X_i,X_j)$$

These results are very easy to be proved and you can find the proofs in any elementary statistic textbook