# finding number of scores, with mean, s.d and Ex^2?

• Apr 7th 2009, 05:24 AM
mightysparks
finding number of scores, with mean, s.d and Ex^2?
This is a question I'm having trouble with:
A set of scores has a mean of 35 and a standard deviation of 13. The sum of the scores squared is 8364.
Calculate the number of scores in this set.

I don't even know where to start! Any help is appreciated, thanks.
• Apr 7th 2009, 05:51 AM
mr fantastic
Quote:

Originally Posted by mightysparks
This is a question I'm having trouble with:
A set of scores has a mean of 35 and a standard deviation of 13. The sum of the scores squared is 8364.
Calculate the number of scores in this set.

I don't even know where to start! Any help is appreciated, thanks.

Sample variance:

$Var(X) = \frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n} = \frac{\left(\sum_{i=1}^n x_i^2\right) - 2 \overline{x} \left( \sum_{i=1}^n x_i \right) + n \overline{x}^2}{n}$

$= \frac{\sum_{i=1}^n x_i^2}{n} - 2 \overline{x} \frac{\sum_{i=1}^n x_i}{n} + \overline{x}^2$

$= \frac{\sum_{i=1}^n x_i^2}{n} - \overline{x}^2$.

Therefore $13^2 = \frac{8364}{n} - 35^2$. Solve this for $n$.