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The mean and standard deviation of a set...

The mean and standard deviation of a set of `n_1`, observations are `bar x_1 and s_1` ,respectively while the mean and standard deviation of another set of `n_2` observations are `bar x_2 and s_2`, respectively. Show that the standard deviation of thecombined set of `(n_1 + n_2)` observations is given by `S.D.=sqrt((n_1(s_1)^2+n_2(s_2)^2)/(n_1+n_2)+(n_1 n_2(( bar x )_1-( bar x )_2)^2)/((n_1+n_2)^2))`

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Knowledge Check

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