Standard deviation

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September 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

$0.68=\frac{{xi-3.07}^2}{6}$
$<br /> <br /> xi=5.0899$ or $xi=1.051$

Guys l am stuck here. It seems like l am in a vicious cycle. What should l do ?
September 30th 2009, 03:31 AM
Deadstar

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

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

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

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