Sixty Five Thousand Either Way

You keep one HyperLogLog per day of unique visitors, sized at m=16384m = 16384 registers. Yesterday's sketch reports 8,000,0008{,}000{,}000 distinct visitors. The estimator's relative standard error is

σrel≈1.04m\sigma_{rel} \approx \frac{1.04}{\sqrt{m}}

and the analysis stores 5 bits per register. What is the one standard error band around that estimate, and how much memory does one day's sketch occupy?

A

About ±8,125\pm 8{,}125 visitors, in about 10 KB.

B

About ±65,000\pm 65{,}000 visitors, in about 10 KB.

C

About ±650,000\pm 650{,}000 visitors, in about 10 KB.

D

About ±65,000\pm 65{,}000 visitors, in about 16 KB.