Combined mean and standard deviation -illustration, Mathematics

Combined mean

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)

 

                        2267_Combined mean.png

 

 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(n1)              600 hours (x1)  hours (s1)

               50 (n1)             520 hours (x2)  30 hours (s2)

Combined mean = (40(600) + 50 (520))/(40 + 50)

=50,000/90

= 555.56

Combined standard deviation

 

              825_Combined mean 1.png

Posted Date: 2/18/2013 1:10:20 AM | Location : United States







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