Find the variance and standard deviation.

{3, 3, 4, 5, 5}

Question

Find the variance and standard deviation. 

{3, 3, 4, 5, 5}

anonymous · Answer

I know the mean is 4 if that helps any in the problem

kirbykirby · Answer

So the standard deviation is found using the formula:

$$ \large s=\sqrt{\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2}$$

kirbykirby · Answer

the variance is simply the square of that, so 
$$ \large s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2$$

anonymous · Answer

Okay thanks, so what would i plug in in those variables?

kirbykirby · Answer

$x_i$ are the individual data points, and $\bar{x}$ is the mean. $n$ is the number of data points in your set (there are 5 in your set ).

$$\large s^2=\frac{1}{5-1}\left( (3-4)^2+(3-4)^4+(4-4)^2+(5-4)^2+(5-4)^2 \right) $$

kirbykirby · Answer

you're subtracting each data point with the mean, 4, then squaring that result. Then you add up of those of results together (I just realized I made a typo on the second sum above... it should be $\large (3-4)^2$, not $\large (3-4)^4$).