The correct probability distribution / way to analyze daily changes

Question

I am working on a report which is being sent through to end users that should flag to them any "large changes" in the day-to-day values for the past 30 days for something we would assume the day-to-day differences to have a mean of zero.

So, assume we have the following data:

Day:    Change from previous day:
1       -40
2       30
3       15
4       12
5       -34
6       -2
...
30      12

And they don't care about the direction of the change, just to flag any day where the change is of a "statistically significant" magnitude.

I'm curious as to how to calculate the statistics for this properly / what distribution would best be used to assign probability levels for this set of data.

What has been proposed is to, firstly, look at the square of the changes (rather than the original values since all we care about is magnitude):

1. To calculate the std dev as $\sqrt{ \dfrac{\sum \left( x_i - 0 \right)^2 }{29}}$ - In other words assume a zero expected value
2. To Calculate the std dev as $\sqrt{ \dfrac{\sum \left( x_i - \bar{x} \right)^2 }{29}}$ - In other words, use the mean we would calculate for this sample

And then to take each day's value and divide it by this std_dev to calculate it's magnitude.

I have quite a few problems with a few things here, but especially idea #2 since I believe the mean SHOULD BE ZERO.

Generally speaking, what is the correct way to analyze deltas with an expected value of zero and what distribution would you use for a 30-sample data-set to find statistically significant values?

I hope this makes sense, but, if not, please let me know where I could clarify more.

THANKS!!!