If ni, n2 are the sizes,¯x, x, the means, and o1, 0, the standard deviations of two series, tlhen the standard deviation o of the conmbined series of size 11 + n2 is given by : o² =, (m, (0,² + dif) +...

Prove the theorem

Extracted text: If ni, n2 are the sizes,¯x, x, the means, and o1, 0, the standard deviations of two series, tlhen the standard deviation o of the conmbined series of size 11 + n2 is given by : o² =, (m, (0,² + dif) + 12 (0,² + d$) ] , 1l1 + N2 where d = x1 – î, d2 = ã2- I and = 1l1 X1 + 112 x2 l1 + 112 X2 - x and F is the mean of the combined series. %3D |