For a group of 50 male workers, the mean and the standard deviation of their daily wages are Rs . 630 and Rs . 90 respectively and for a group of 40 female workers these are Rs . 540 and Rs . 60 respectively. Then, the standard deviation of all these 90 workers is

Step-by-step solution

n 1 = 50 ,   x ¯ 1 = 630 ,   σ 1 = 90 n 2 = 40 ,   x ¯ 2 = 540 ,   σ 2 = 60 x ¯ = 50 × 630 + 40 × 540 50 + 40 = 3150 + 2160 9         = 5310 9 = 590 Now, d 1 = x ¯ 1 − x ¯ ,   d 2 = x ¯ 2 − x ¯ d 1 = 630 − 590 = 40 d 2 = 540 − 590 = − 50 S.D. of the 90 workers = n 1 ( σ 1 2 + d 1 2 ) + n 2 ( σ 2 2 + d 2 2 ) n 1 + n 2 = 50 ( 8100 + 1600 ) + 40 ( 3600 + 2500 ) 90 = 5 ( 9700 )