Noise in an average

Variances of independent trades add up.

1. The variance of the total is $64$ times the variance of one trade, so the total has standard deviation $12\times \sqrt{64}$.
2. The average divides the total by $64$.
3. This gives a standard deviation of $12÷\sqrt{64}$, where $\sqrt{64}=8$.
4. So the standard deviation of the average is $12÷8=1.5$.

Answer: $1.5$