1. ## 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

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

$\displaystyle xi=5.2541$ or $\displaystyle 0.8859$

Boys

$\displaystyle 0.68=\frac{{xi-3.07}^2}{6}$
$\displaystyle xi=5.0899$ or $\displaystyle xi=1.051$

Guys l am stuck here. It seems like l am in a vicious cycle. What should l do ?

2. I'm not 100% sure of this but I think you want to find the pooled standard deviation which is found using this formula...

$\displaystyle s^2 := \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{(n_1 - 1) + (n_2 - 1)}$

Where $\displaystyle s$ = pooled standard deviation
$\displaystyle s_1$ = standard deviation of females
$\displaystyle n_1$ = number of females
$\displaystyle s_2$ = standard deviation of males
$\displaystyle n_2$ = number of males