Combined mean
Assume m be the combined mean
Assume x_{1} be the mean of first sample
Assume x_{2} be the mean of the second sample
Assume n_{1} be the size of the 1^{st} sample
Assume n_{2} be the size of the 2^{nd} sample
Assume s_{1} be the standard deviation of the 1^{st} sample
Assume s_{2} be the standard deviation of the 2^{nd} sample
∴ Combine mean = (n_{1}x_{1} + n_{2}x_{2})/(n_{1}n_{2})
Illustration
A sample of 40 electric batteries described a mean life span of 600 hours along with a standard deviation of 20 hours.
Other sample of 50 electric batteries described a mean lifespan of 520 hours along with a standard deviation of 30 hours.
If these two samples were combined and utilized in a given project simultaneously, find out the combined new mean for the larger sample and hence find out the combined or pulled standard deviation.
Size x s
40(n_{1}) 600 hours (x_{1}) hours (s_{1})
50 (n_{1}) 520 hours (x_{2}) 30 hours (s_{2})
Combined mean = (40(600) + 50 (520))/(40 + 50)
=50,000/90
= 555.56
Combined standard deviation