Assume m be the combined mean
Assume x1 be the mean of first sample
Assume x2 be the mean of the second sample
Assume n1 be the size of the 1st sample
Assume n2 be the size of the 2nd sample
Assume s1 be the standard deviation of the 1st sample
Assume s2 be the standard deviation of the 2nd sample
∴ Combine mean = (n1x1 + n2x2)/(n1n2)
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(n1) 600 hours (x1) hours (s1)
50 (n1) 520 hours (x2) 30 hours (s2)
Combined mean = (40(600) + 50 (520))/(40 + 50)
Combined standard deviation