# Error Propagation of standard deviation?

I have the following problem:

I do measurements with technical triplicates and biological duplicates. So I prepare the same sample two times and measure each one three times.

This gives me an average value of each duplicate with a standard deviation, calculated by the technical triplicates.

E.g. $$0,23 \pm 0,07\ \text{ and }\ 0,20 \pm 14.$$

Now I want to determine the total average and its error. And here I get confused: with the error propagation I can calculate the error for the average

$$\Delta x=\frac{1}{2}\sqrt{(Δx_1)^2+(Δx_2)^2}=0,16,$$

but there is also the standard deviation of the two values (~0,014).

I am wondering now, how I can combine both values to the error of the total average. Taking just the error propagation seems wrong to me, especially when the duplicate measurements differ greatly.