Determine proper coefficients for the transfer function
Your are basically designing a lowpass filter in order to suppress the noise to some extend. For now I will assume that you are dealing with white noise, so a flat frequency spectrum with a time average of zero. But the value you are after is 26, which in the frequency spectrum is just a spike at zero Hertz. So in order for your filter to recover this value a good as possible it should be stable and have unity gain at zero Hertz.

Fixing $a\in(0,1)$ should ensure that the transfer function has a pole inside the unit disk and therefore be stable. In order to ensure the unity gain at zero Hertz you need to evaluate $H(z)$ at zero Hertz. In order to evaluate a discrete time transfer function at a frequency you can use $z=e^{j\,\omega\,T}$, with $\omega$ the frequency is radians per second and $T$ the sample time. So for zero Hertz/radians per second you get $z=1$. So evaluating $H(z)$ at this $z$ value gives

$$
H(1) = \frac{b}{1 - a}.
$$

This is only equal to one (unity) if $b=1-a$. So if you used $a=0.5$ then indeed it should be that $b=0.5$.