Computing the derivative from a set of real-time data?
Depending on the level of noise you expect to encounter on your signal, you might actually be able to use the finite differencing you suggest, originally. If you want to know the general trend of your data upward or downward, sum together the, in your case, 24, differences. So, lets say that you have some metric, $D$, for your signal. Lets say that for a given signal, $x[n]$, the first order difference is denoted as $x\prime[n]$ (and is, of course, one entry shorter than $x[n]$). Define $D$ as

$$ D = \sum_{n=0}^{N-2} x\prime[n] .$$

Then, classify your signal as uptrending or downtrending via

$$ D &gt; 0 ~\therefore~\uparrow$$
$$ D &lt; 0 ~\therefore~\downarrow$$

I made some basic assumptions about the nature of the signals in question. I just did the most basic analysis and thought, well, maybe just use a ramp, $r[n]$, corrupted by some noise, $z[n] \sim \mathcal{N}(0,\sigma^2)$. This may or may not be the situation you're looking at, so you'll need to adjust accordingly and see what works for you. But my final model was just the simple
$$x[n] = r[n] + z[n]$$ 
for the length you gave, $N = 25$.

I went ahead and ran some experiments in MATLAB. I used the following code:

experiments = 1000;
N = 25;

slope_min = -2;
slope_max = 2;
slope_range = slope_max - slope_min;
noise_level = 2;


for i=1:experiments

    slope(i) = slope_range*rand(1)+slope_min;
    r = slope(i)*(1:N);
    z = noise_level.*randn(1,N);

    x = r + z;

    diffsum(i) = sum(diff(x));
end


First, let me show what some of the signals look like...



So, I varied the variance of the noise signal, $z[n]$ and recorded the following correlations between the true slope (up or down trend) of $r[n]$ in comparison with the metric we defined above, $D$. If $D$ does a good job determining the trend of the signal, we should see a strong correlation between downtrends (negative slopes) and negative $D$ and uptrends (positive slopes) and positive $D$. 





We can see from the above that $D$ does seem to do a decent job. As the noise level increases (or the signal moves further away from our model), the correlations are not as strong. Try it out on your signals, see if does anything for you.