The most accurate way to plot the variance would be to take daily weighted price. Choosing the smoothed data is much better than plotting variations on the minute by minute or hour by hour.
No, it's just different. If you want to do arbitrage trading then tracking second to second variation will give you the best result.
The point is that no one is doing arb trading otherwise the spread wouldn't exist! (or it is probably some whales with priority wires taking advantage of the spread). So in the context of tracking the price variance, one would choose daily values since this variance has existed for over 2 months.