Hmm... if you have the total acceleration time and the total deceleration time, you can simply add them as two datasets (correlations do not matter).
Let ta be the total (positive) acceleration time steps. Let aa be the average (positive) acceleration and σa the standard deviation in this dataset.
Define the same parameters with d for deceleration.
Let t be the total time = number of steps: t=ta+td
Your average acceleration (positive+negative, without superscript) is then given by
[tex]\bar{a} = \frac{a^a t^a + a^d t^d}{t^a+t^d}[/tex]
The standard deviation can be calculated via
[tex]t \sigma^2 = \sum_{i,a_i>0} (a_i-\bar{a})^2 + \sum_{i,a_i<0} (a_i-\bar{a})^2[/tex]
where the first sums run over all time steps with positive acceleration and the second runs over all with negative acceleration. N is the total number of steps. This can be simplified:
[tex]t \sigma^2 = \sum_{i,a_i>0} (a_i-a^a + a^a - \bar{a})^2 + \sum_{i,a_i<0} (a_i-a^d + a^d-\bar{a})^2[/tex]
[tex]t \sigma^2 =\sum_{i,a_i>0}<br />
\left((a_i-a^a)^2 + (a^a - \bar{a})^2 + 2(a_i-a^a)(a^a-\bar{a})\right)<br />
+ \sum_{i,a_i<0} <br />
\left((a_i-a^d)^2 + (a^d - \bar{a})^2 + 2(a_i-a^d)(a^d-\bar{a})\right)[/tex]
In both sums, the first expression is simply the standard deviation of the individual parts. [itex](a^a-\bar{a})[/itex] is constant, and the average ai is simply aa (same for d) so those terms vanish. The middle term is independent of i, so the sum just gives a factor of ta and d respectively.
[tex]t \sigma^2 =t^a \sigma^a + t^d \sigma^d<br />
+ t^a (a^a - \bar{a})^2)<br />
+ t^d (a^d - \bar{a})^2)<br />
= t^a \sigma^a + t^d \sigma^d + t\bar{a}^2 + t^a {a^a}^2 + t^d {a^d}^2 - 2t^a a^a \bar{a} - 2t^d a^d \bar{a}[/tex]
Using the expression for [itex]\bar{a}[/itex], this gives
[tex]t \sigma^2 = t^a \sigma^a + t^d \sigma^d+ t^a {a^a}^2 + t^d {a^d}^2 - t\bar{a}^2[/tex]
And that can be calculated, as all parts are known.If you do not now the umber of acceleration / deceleration steps: Maybe you can calculate the average acceleration based on the initial and final velocity and the total number of steps. This will allow you to calculate ta and td as well.