# Standard deviation

• Sep 29th 2009, 08:21 PM
nyasha
Standard deviation
The GPA for a class of ten females and seven males are recorded. The mean GPA of females is 3.07 and the standard deviation is 0.53. The mean GPA for males is also 3.07 and the standard deviation is 0.68. What is standard the deviation for all students ?

Attempt to solution:

Girls

$0.53=\frac{{xi-3.07}^2}{9}$

$xi=5.2541$ or $0.8859$

Boys

$0.68=\frac{{xi-3.07}^2}{6}$
$

xi=5.0899$
or $xi=1.051$

Guys l am stuck here. It seems like l am in a vicious cycle. What should l do ?
• Sep 30th 2009, 03:31 AM
$s^2 := \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{(n_1 - 1) + (n_2 - 1)}$
Where $s$ = pooled standard deviation
$s_1$ = standard deviation of females
$n_1$ = number of females
$s_2$ = standard deviation of males
$n_2$ = number of males