combined variance



combined variance


nx,ny    the number of people 

X mean, Y  mean, z  mean    means

variance   variance

standard deviation    standard deviation the positive square root of the variance

for example


group a

the number of people  - 35
mean  - 75
standard deviation  - 25



group b

the number of people  - 55
mean  - 95
standard deviation  - 45



combined mean = (35·75+55·95) / (35+55) = 87.22


826500 (2^25 + 2^75) · 35 + (2^45 + 2^95) · 55
1576 = 7607.33  -  ------------ = 2^(87.22) -  ------------------------------------------------------------ = even combined variance
90 35 + 55




one number was added to the data the number 60 what will be the new standard deviation

combined mean = (90·87.22+1·60) / (90+1) = 86.92










825397.78 (1576 + 2^86.92) · 90 + (2^0 + 2^60) · 1
1515.22 = 7555.01  -  ------------ = 2^(86.92) -  ------------------------------------------------------------ = even combined variance
91 90 + 1




38.93 = standard deviation







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