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!