Uh... how so? I mean, I understand you're argument: you're basically saying that the sample size is too low because of these two outliers and that the aggregate burn rate is much less. Which is true, but IMHO completely misses the point.
The goal here isn't to measure the burn rate with precision, it's to figure out what the risk is of Facebook running out of money. And in that context, dropping a quarter of everything you have, without warning, on two very large purchases of questionable[1] real value seems like a really important data point to me.
[1] Lest I be misunderstood, I'm not saying that they are without value. I'm saying that the value isn't at all obvious even to expert observers -- two weeks ago, had someone suggested that facebook buy a $1B photo startup or $550 worth of patents from Microsoft they probably would have been laughed at.
The fact that they've spent 25% of their cash in one week doesn't really tell us how much they have spent in the past, nor if they are going to(or even likely to) spend as much in the next few weeks.
The reason is that these are one-off purchases. Burn rate is typically used for recurring expenses like office rent, salaries etc. For example, if your startup's burn rate is 100K/mo and has 1 million in cash, it will need another funding event before 10 months(if everything remains the same).
Regarding the purchases, I think Zuckerburg knows much more than we do. He has proved to be a very shrewd negotiator (see the IPO terms) and there seems to be more around this than has been let on, especially regarding the patents and chances of Google integrating Instagram into G+ and turning it instantly into a photosharing hub.
Considering they made two one-off huge burns in a week, what are the odds they will manage not to make two other similar burns and spend another 25% of their reserves? If they had the need to make them, what are the chances they'll need to do it again and what the penalties will be for not making them?
I agree the burn rate is not hugely impacted by these two events, but they signal the burn rate is not constant. If in early April we knew Facebook had money for, say, 1 year, we now know they have money for 8 months.
You simply recapitulated your sample size argument. Did you read what I wrote? There's a difference between computing an average and computing the variance. Big spending sprees may not affect the former, but the clearly affect the latter. And from an investing perspective right now, given the impending IPO, it's the latter that is more important. "What is the risk that Facebook will run out of money in the next N days?" is not a question that can be answered by multiplying N by their average burn rate!