I have:
A1: {3, 5, 6} and A2: {3, 4, 6, 8}
Avg A1: 4.(6)
Std.Deviation A1: 1.247
Avg A2: 5.25
Std. Deviation A2: 1.92
Merging A1 and A2, we get
A12: {3, 3, 4, 5, 6, 6, 8}
Avg A12: 5
Std. Deviation A12: 1.69
I want to be able to obtain those values (avg and std. deviation for A12), having only the following information about A1 and A2:
A1
No. Elements: 3
Avg A1: 4.(6)
Std.Deviation A1: 1.247
A2
No. Elements: 4
Avg A2: 5.25
Std.Deviation A2: 1.92
Average is easy, (4.(6)*3 + 5.25*4)/7 = 5
But I seem to be unable to calculate the correct std. deviation value. I can only use the above information. Any ideas?