# Thread: Standard Deviation

1. ## Standard Deviation

The weight, in grams, of 10 bags of sweets are as follows:
251, 253, 254, 249, 249, 248, 250, 251, 252, 247

If it is assumed that the weights of the 10 bags of sweets in the preceding questions represent the entire population of weights in which we are interested, what is the standard deviation of these weights?
• 2.11g
• 4.45g
• 4.93g
• 2.22g
• None of the above.
any idea how to work out the standard deviation?

2. Originally Posted by chungkayan
any idea how to work out the standard deviation?

Yes,
$\displaystyle var(Y)=E(Y^2)-[E(Y)]^2$

So
$\displaystyle E(Y^2)=\frac{251^2+253^2+254^2+249^2+249^2+248^2+2 50^2+251^2+252^2+247^2}{10}$$\displaystyle =62704.6$

$\displaystyle E(Y)={251+253+254+249+249+248+250+251+252+247}{10} =250.4$

So $\displaystyle var(Y)=62704.6-250.4^2=4.44$
and standard deviation is the square root of variance....
so $\displaystyle \sigma =\sqrt{4.44}=2.107131$

which could be rounded up to 2.11

3. Thanks for the help. I get it now. this is the formula for working every standard deviation sum, right?