Calculating a weighted mean/SD of x number of means/SDs?

#1
I'm doing some data analysis of patients undergoing cardiac ablation procedures. We use our equipment to collect electrical data from inside patients' hearts in quite high resolution. I'm struggling to see if the following can be done:

I have 10 patients. We have some proprietary software that has used the data collected from a specific region X the hearts of each of the 10 patients and summarised it for us. Because of heterogeneity in patients, region X in one patient may have 40 separate data points, in another 90 points, in another 17 points. The software has given me a mean of all points for each patient, the SD and the n number (ie. how many points were used to calculate the mean/SD) but NOT the individual values for each of the points. For this case, the values represent the velocity of conduction of electrical signal within the heart in this specific region in (centimetres per second).

So for the first two patients as an example, I have:

P1
Mean = 2.38cm/s
SD = 0.5
n = 45

P2
Mean = 3.56cm/s
SD = 1.3
n = 17

And so on, for all 10 patients.

What I want to know is, is it possible to calculate the mean of the means and to get an SD for the entire cohort of 10 patients, if you have the number of points used to calculate the individual means but NOT the individual values for each of those points? Perhaps you weight things so that those with higher n/lower SD have greater representation? I don't know if this is possible, but your help would be much appreciated!
 
#3
Sorry, all I’m trying to say is that for some of the mean/SD values, the number of points used to obtain those values is 40, for other values it’s 17. Each of the 10 means/SD has a different number of points used to calculate them. I need to subsequently calculate the man of all the means and an overall SD with just these three data points - mean, SD and n.