For a group of 50 male worker, the mean and standard deviation of their weekly wages are Rs 63 and - Maths - Statistics

Question

For a group of 50 male worker, the mean and standard deviation
of their weekly wages are Rs 63 and Rs 9 respectively and for a
group of 40 female workers, the measures are respectively Rs 54 and
Rs 6 Find the standard deviation for combined group workers

Priyanka Kedia · Accepted Answer

Given, the mean of weekly wages of male workers x1=63The mean of
weekly wages of female workers x2=54And, the standard deviation of
weekly wages of male workers σ1=9The standard deviation of
weekly wages of male workers σ2=6Thus,The combined mean x=n1
x1+n2 x2n1+n2 =50×63+40×5450+40 =3150+216090 =531090
=59And,d1= x- x1=59-63=4d2= x- x2=59-54=5The combined standard
deviation σ=n1 σ12+d12+n2 σ22+d22n1+n2
=50×92+42+40×62+5250+40
=50×81+16+40×36+2590 =4850+244090 =81 =9Thus,the
combined mean is 59 and the combined standard deviation is 9

For a group of 50 male worker, the mean and standard deviation of their weekly wages are Rs 63 and Rs 9 respectively and for a group of 40 female workers, the measures are respectively Rs 54 and Rs 6 . Find the standard deviation for combined group workers.